MILBURN, Circuit Judge.

Plaintiffs appeal the district court's grant of summary judgment to defendants City of Dayton and its police chief, James E. Newby in this 42 U.S.C. § 1983 action brought to recover damages for the death of one individual and for injuries to another individual inflicted by an off-duty police officer, defendant Roger W. Waller, and his friend, defendant Dennis Michael. Defendants cross-appeal the district court's denial of summary judgment on plaintiffs' state law negligence claim. On appeal, the issues are (1) whether there is a genuine issue of material fact as to whether the off-duty police officer was acting under color of state law when he shot and killed one man and injured another, and if so (2) whether the City of Dayton and its chief of police may be held liable for the injury inflicted, and (3) whether the district court properly denied summary judgment to the police chief on plaintiffs' state law negligence claim. For the reasons that follow, we affirm in part and reverse in part.

I.

In September 1988 Roger W. Waller was a police officer for the City of Dayton, Ohio. His full-time assignment was to coordinate the department's Drug Hotline Volunteer Program. The duties of this assignment included scheduling volunteers to answer telephones, training volunteers, answering telephones, and distributing program reports. Generally, citizens would call the hotline to report suspicious drug-related events, such as suspected drug houses. The volunteers would fill out a report and give the report to Officer Waller. Officer Waller would make sure the information on the report was complete, and sometimes he would seek to verify the information by travelling to the location of the reported drug house and checking the address or observing the house to see if there were any indications of drug trafficking. However, on these verification trips, Officer Waller would never do anything other than observe for a short period of time. He would not talk to anyone, and he would not attempt to buy drugs from the houses. A sergeant within the police department asked him to make these verification trips. If a citizen complaint appeared valid, Officer Waller would submit his report to officers who could initiate further investigations and warrants if needed. Officer Waller had no other duties. His responsibilities were administrative, and he was not a patrol officer or detective. Other than short verification investigations, Officer Waller was not authorized to conduct any drug enforcement activities, such as controlled purchases, investigations, or raids.

September 15, 1988 was Officer Waller's scheduled day off. He was at home with his friend Dennis Michael and was having a furnace installed. After finding out what Waller's job was, the man installing the furnace complained about a house in his neighborhood that he suspected of being a drug house. When Waller said he would investigate, Michael reminded Waller that he had told Waller about a drug house in his old neighborhood where his daughter had been stuck by a dirty needle. Waller told Michael that he could point the house out to him, and together they could investigate.

When Waller and Michael began their investigation, Waller was not on duty, and the police department did not authorize or know about the investigation. Waller was not wearing his uniform, but he was carrying his badge and identification in his pocket and his service 9 mm pistol and radio in his belt. Waller was also carrying a Mac-11 machine gun under his jacket in a shoulder holster. Michael, who was not a police officer, was carrying a shotgun. The Dayton Police Department's firearms policy allowed, but did not require, police officers to carry their 9 mm pistols while off duty. However, the firearms policy prohibited off-duty officers from carrying any other firearms.

After finding no activity at the house mentioned by the furnace installer, Waller and Michael went to Michael's old neighborhood. Michael showed Waller the suspected drug house, and the two walked past the house. They watched the house for approximately 10 to 30 minutes. Observing nothing, Waller "decided to go down and try to make a buy at the door." J.A. 340. As he was walking toward the house, a girl walked out on the porch. Waller identified himself as a police officer by displaying his badge and identification card and told the girl to go away because he "was going to bust the house." J.A. 341.

Waller then walked to the screen door and addressed the two persons sitting in the house, Lawrence Eugene Hileman and Jerry L. Smith. Waller told them he wanted to buy some crack cocaine, but Hileman and Smith started laughing and stated they did not sell crack cocaine. Hileman then motioned for Waller to enter the house, which Waller did. Upon entering, Waller identified himself as "drug enforcement" and asked Hileman and Smith for some identification. Michael also entered the house. Waller asked where the drugs were and stated, "You know, somebody is going to go to jail here if we don't find out where the drugs are." J.A. 353-54. Waller then turned toward Hileman, and the Mac-11 machine gun Waller was carrying discharged, hitting Hileman. Waller left the house, and Michael shot Smith twice with the shotgun. As a result of these shootings, Hileman died and Smith was seriously injured.

Waller pleaded guilty to murder and felonious assault. Michael pleaded guilty to involuntary manslaughter and felonious assault.

Between 1981 and 1983, there had been several reports that Officer Waller was participating in drug trafficking. Plaintiffs contend that the police department failed to investigate these allegations. Defendants contend, however, that these allegations were investigated and found to be baseless.

In 1985, Officer Waller obtained the Mac-11 machine gun used to kill Hileman, and was told by the Bureau of Alcohol, Tobacco and Firearms that his application to possess that weapon must be submitted to the local chief of police for signature. The former chief of police for the City of Dayton refused to sign the application unless Waller rendered the machine gun nonfireable and only used it for display. However, when James E. Newby became chief of police for the City of Dayton, Waller presented the application to Newby, and he signed it.

In July 1990, Smith and the executrix for Hileman's estate filed this 42 U.S.C. § 1983 action against Waller, Michael, the City of Dayton, and Chief Newby. Plaintiffs' complaint also alleged state law negligence and intentional tort claims based on Waller and Michael's actions on September 15, 1988, and on Chief Newby's signing of the application allowing Waller to possess the machine gun that was used by Waller to kill Hileman on September 15, 1988.

On August 17, 1993, the district court granted summary judgment to defendants Dayton and Newby on plaintiffs' 42 U.S.C. § 1983 claims, holding that Waller was not acting under color of state law, and therefore plaintiffs did not have a viable § 1983 claim against defendants City of Dayton and Newby. The district court also held that even if Waller had been acting under color of state law, plaintiffs would still not have viable § 1983 claims against the City or Newby because (1) there was no evidence that the City had a custom or policy which was the moving force behind the shooting of Hileman and Smith, and (2) there was no evidence tending to show that Newby encouraged or participated in the shooting of Hileman and Smith. As to plaintiffs' state law claims, the district court held that the City of Dayton was immune from liability under Ohio Revised Code Annotated § 2744. However, as to defendant Newby, the district court held that there was a genuine issue of material fact as to whether his actions in signing the application that allowed Waller to possess the machine gun were reckless or wanton, which would have negated his immunity defense. Therefore, after the district court's ruling, the only remaining claims were the one state law claim against Newby and the claims against Waller and Michael.

Pursuant to Federal Rule of Civil Procedure 54(b), the district court determined that there was no just reason for delay and directed that final judgment be entered in favor of the City, dismissing with prejudice all of plaintiffs' claims against the City. The district court also directed that final judgment be entered in favor of defendant Newby, dismissing with prejudice the § 1983 claim and the state claim predicated on the actions of Michael and Waller, but not the state claim predicated on Newby's act of signing the machine gun application. Plaintiffs filed a timely notice of appeal, and 15 days later defendants City of Dayton and Newby filed a cross-appeal.

II. A.

Plaintiffs challenge the district court's grant of summary judgment to the City of Dayton and Chief Newby on the § 1983 claim. This court reviews a district court's grant of summary judgment de novo. Brooks v. American Broadcasting Cos., 932 F.2d 495, 500 (6th Cir. 1991). Summary judgment is appropriate where there is no genuine issue of material fact and the moving party is entitled to judgment as a matter of law. Fed.R.Civ.P. 56(c). In our review, we must view all facts and inferences in the light most favorable to the nonmoving party. Boyd v. Ford Motor Co., 948 F.2d 283, 285 (6th Cir. 1991), cert. denied, ___ U.S. ___, 112 S.Ct. 1481, 117 L.Ed.2d 624 (1992).

As an initial matter, plaintiffs argue that the district court erred in granting summary judgment because defendants did not challenge the sufficiency of plaintiffs' allegations and presented insufficient facts to refute those allegations. However, that argument relies on a misunderstanding of the distinction between a motion for summary judgment and a motion to dismiss for failure to state a claim. While a motion to dismiss for failure to state a claim is a challenge to the sufficiency of the plaintiff's allegations, a motion for summary judgment is a challenge to the sufficiency of the plaintiff's proof. A motion to dismiss for failure to state a claim argues that even if the plaintiff's allegations are true, the plaintiff is still not entitled to relief under the applicable law. On the other hand, a motion for summary judgment does not accept the plaintiff's allegations as true, but rather argues that the plaintiff cannot prove his claim.

The party seeking summary judgment bears the initial burden of showing the district court that there is an absence of a genuine dispute over any material fact. Celotex Corp. v. Catrett, 477 U.S. 317, 323, 106 S.Ct. 2548, 2552-53, 91 L.Ed.2d 265 (1986). This burden "may be discharged by `showing' — that is, pointing out to the district court — that there is an absence of evidence to support the nonmoving party's case." Id. at 325, 106 S.Ct. at 2554. In order to defeat the motion for summary judgment after the movant has carried its initial burden, the nonmoving party cannot respond by merely resting on the pleadings, but rather the nonmoving party must present some "specific facts showing that there is a genuine issue for trial." Id. at 324, 106 S.Ct. at 2553 (quoting Fed.R.Civ.P. 56(e)). For summary judgment purposes it is irrelevant whether the defendant challenges the sufficiency of the plaintiff's allegations or whether the defendant presents evidence to refute those allegations. Therefore, plaintiffs' argument that defendants' motion for summary judgment should have been denied because defendants did not challenge the sufficiency of plaintiffs' allegations and presented insufficient facts to refute those allegations is meritless.

To prove a claim under 42 U.S.C. § 1983, a plaintiff must establish: (1) that he was deprived of a right secured by the Constitution or laws of the United States, and (2) that he was subjected to or caused to be subjected to this deprivation by a person acting under color of state law. Flagg Bros. v. Brooks, 436 U.S. 149, 155, 98 S.Ct. 1729, 1732-33, 56 L.Ed.2d 185 (1978). A municipality may be held liable under § 1983 if the municipality itself caused the constitutional deprivation. Monell v. Department of Social Servs., 436 U.S. 658, 98 S.Ct. 2018, 2035-36, 56 L.Ed.2d 611 (1978). However, a municipality is not liable under § 1983 for an injury inflicted solely by its employees or agents; the doctrine of respondeat superior is inapplicable. Id. at 691-95, 98 S.Ct. at 2036-38. "`It is only when the "execution of the government's policy or custom . . . inflicts the injury" that the municipality may be held liable under § 1983.'" City of Canton v. Harris, 489 U.S. 378, 385, 109 S.Ct. 1197, 1203, 103 L.Ed.2d 412 (1989) (quoting Springfield v. Kibbe, 480 U.S. 257, 267, 107 S.Ct. 1114, 1119, 94 L.Ed.2d 293 (1987) (O'Connor, J., dissenting)); see also Monell, 436 U.S. at 694, 98 S.Ct. at 2037-38. The local government's policy or custom "must be `the moving force of the constitutional violation' in order to establish the liability of a government body under § 1983." Polk County v. Dodson, 454 U.S. 312, 326, 102 S.Ct. 445, 454, 70 L.Ed.2d 509 (1981) (quoting Monell, 436 U.S. at 694, 98 S.Ct. at 2037-38).

The district court granted summary judgment to the City on two independent bases. The first basis was that Michael and Officer Waller were not acting under color of state law when they shot Hileman and Smith. The second basis was that there was no evidence that the City had a custom or policy that was the moving force behind Officer Waller's decision to shoot Hileman and Smith.

While there may be a question concerning the first basis upon which the district court granted summary judgment to the City, we conclude that the district court properly granted summary judgment on the second basis, i.e., that there was no evidence that the City had a custom or policy that was the moving force behind Officer Waller's shooting of Hileman and Smith. As discussed above, Monell requires that for a municipality to be held liable under § 1983, a municipal policy or custom must be the moving force behind the constitutional injury. "[T]o satisfy the Monell requirements a plaintiff must `identify the policy, connect the policy to the city itself and show that the particular injury was incurred because of the execution of that policy.'" Garner v. Memphis Police Dep't, 8 F.3d 358, 364 (6th Cir. 1993) (quoting Coogan v. City of Wixom, 820 F.2d 170, 176 (6th Cir. 1987)), cert. denied, ___ U.S. ___, 114 S.Ct. 1219, 127 L.Ed.2d 565 (1994).

In this case, plaintiffs argue that the City's alleged failure to investigate information of misconduct on the part of Waller satisfies the official policy requirement. On the other hand, the City contends that the evidence shows that the City did investigate the allegations of misconduct. Regardless of whether the City failed to investigate the allegations of misconduct, and regardless of whether such failure amounted to a policy or custom, plaintiffs have not presented any evidence to indicate that the failure to investigate other unconnected misconduct was the moving force behind the shooting of plaintiffs. Furthermore, although plaintiffs' complaint alleges that the shooting resulted from the City's failure to train Waller and other officers, plaintiffs have not pointed to any evidence in the record that would indicate that the City's training of police officers was inadequate, or that the alleged failure to train resulted from the City's deliberate indifference, both of which are required for failure to train to be actionable. See City of Canton, 489 U.S. 378, 109 S.Ct. 1197. Accordingly, summary judgment for the City was appropriate because there is no indication in the record that a policy or custom of the City caused plaintiffs' alleged constitutional injuries.

The district court also properly granted summary judgment to defendant Newby on plaintiffs' § 1983 claim. A supervisory employee cannot be held liable under § 1983 for the constitutional torts of those he supervises unless it is shown "that the supervisor encouraged the specific incident of misconduct or in some other way directly participated in it." Bellamy v. Bradley, 729 F.2d 416, 421 (6th Cir.), cert. denied, 469 U.S. 845, 105 S.Ct. 156, 83 L.Ed.2d 93 (1984). Plaintiffs have not pointed to any evidence in the record tending to show that Newby encouraged or participated in the shooting of Hileman and Smith. Therefore, the grant of summary judgment to Newby on the § 1983 claim was proper.

B.

We now turn to defendants' cross-appeal of the district court's denial of summary judgment to Newby on the state law negligence claim based on his signing of the machine gun application. Before turning to the merits, we must determine whether we have jurisdiction to consider the cross-appeal.

The jurisdictional deficiency raised by the plaintiffs concerns the timeliness of the filing of defendants' notice of cross-appeal. Plaintiffs have filed a motion to dismiss the cross-appeal based on defendants' late filing of their notice of cross-appeal, and we previously issued an order to show cause why the cross-appeal should not be dismissed due to the untimely notice.

A timely notice of appeal is a mandatory and jurisdictional prerequisite which this court can neither waive nor extend. Browder v. Director, Department of Corrections of Ill., 434 U.S. 257, 264, 98 S.Ct. 556, 560-61, 54 L.Ed.2d 521 (1978). A notice of appeal for a cross-appeal must be filed "within 30 days after the date of entry of the judgment or order appealed from" or "within 14 days after the date when the first notice was filed, . . . whichever period last expires." Fed.R.App.P. 4(a)(1) (3). The judgment and denial of summary judgment in this case were entered August 17, 1993. No time tolling motion was filed. Plaintiffs filed their notice of appeal on September 15, 1993, exactly 30 days after the entry of final judgment. Defendants' notice of cross-appeal was stamped filed on Thursday, September 30, 1993, 45 days after entry of judgment, and 15 days after the filing of plaintiffs' notice of appeal. See Fed.R.App.P. 26(a) (directing that in computing filing times the day of the event from which the designated period begins to run is not counted but the last day of the period is counted unless it is a weekend or holiday). Therefore, if the stamped filing date is the date upon which the notice of cross-appeal is deemed to have been filed, then the notice was filed one day late, and this court would arguably not have jurisdiction over the cross-appeal. See Cyrak v. Lemon, 919 F.2d 320, 323-24 (5th Cir. 1990) (applying requirements of Fed.R.App.P. 4(a)(3) strictly and dismissing cross-appeal). But see Texport Oil Co. v. M/V Amolyntos, 11 F.3d 361, 366 (2d Cir. 1993) (holding that requirements of Fed.R.App.P. 4(a)(3) are more a matter of practice than jurisdictional prerequisites and exercising discretion to entertain cross-appeal even though filed one day late).

However, defendants have presented an affidavit of counsel that indicates that the date stamped on the notice of cross-appeal is not actually the date that notice was filed. Defense counsel's affidavit states that she was advised by telephone by the district court clerk's office that no filing fee was required to file a notice of cross-appeal. A runner from her office then took the notice of cross-appeal without a filing fee to the clerk's office for filing on September 29, 1993. Upon presenting the notice of cross-appeal for filing, the runner was apparently advised by the clerk's office that the notice could not be accepted without a $105 filing fee. The runner returned to the law firm's office, collected a $105 check, and returned to the clerk's office. However, by that time the clerk's office had closed for the day. The notice of cross-appeal along with the check were then presented to the clerk's office the following day, September 30, 1993, at which time the notice of cross-appeal was stamped filed.

"Where a notice of appeal is physically placed in the hands of the clerk's office within the prescribed time limit for filing, but the fee is not paid and filing does not take place until the limit expires, the notice may be treated as timely." Gee v. Tenneco, Inc., 615 F.2d 857, 859 (9th Cir. 1980); see also Parissi v. Telechron, Inc., 349 U.S. 46, 46-47, 75 S.Ct. 577, 577, 99 L.Ed. 867 (1955) (per curiam). In this case, the clerk's office refused to accept the notice of cross-appeal within the prescribed 14 day time limit solely because the runner did not have the filing fee, and therefore the notice of cross-appeal should be treated as if timely filed. Accordingly, defendants have shown good cause why their cross-appeal should not be dismissed for lack of a timely filed notice of cross-appeal, and therefore plaintiffs' motion to dismiss on the ground that the notice was not timely filed should be denied.

Federal Rule of Civil Procedure 54(b) provides a means in multiple-party or multiple-claim actions, such as this case, by which appeals may be taken from final decisions on individual claims without waiting for final decisions on the rest of the claims. The district court made the required findings and properly certified the grant of summary judgment to the City for immediate appeal under Rule 54(b), but it did not certify under Rule 54(b) the denial of summary judgment to Newby on plaintiffs' state law negligence claim.

However, in their statement of appellate jurisdiction, defendants seem to argue that there is appellate jurisdiction over the denial of summary judgment on the negligence claim because we have appellate jurisdiction over the grant of summary judgment. We have stated: "Where . . . an appeal from a denial of summary judgment is presented in tandem with an appeal from a grant of summary judgment, this court has jurisdiction to review the propriety of the district court's denial of summary judgment." Garner v. Memphis Police Dep't, 8 F.3d 358, 363 (6th Cir. 1993) (citing Nazay v. Miller, 949 F.2d 1323, 1328 (3d Cir. 1991)). Thus, since both the plaintiffs' appeal and defendants' cross-appeal arise out of the same set of facts, we have jurisdiction to hear the defendants' cross-appeal.

We hold that the district court erred in failing to grant summary judgment to defendant Newby on the negligence claim. Although defendant Newby signed Officer Waller's application to possess the Mac-11 machine gun used to kill Hileman, the record is devoid of any causation with regard to Newby's signing the application and the killing of Hileman. Therefore, summary judgment should have been granted to defendant Newby on plaintiffs' negligence claim.

III.

For the reasons stated, the district court's grant of summary judgment to the City of Dayton and James E. Newby on plaintiffs' section 1983 claims is AFFIRMED, but the district court's failure to grant summary judgment for defendant Newby on plaintiffs' negligence claim is REVERSED, and this case is REMANDED for further proceedings consistent with this opinion.