BERDON, J.

The defendant, Gerald Gerardi, was convicted of possession of a machine gun for an aggressive and offensive purpose in violation of General Statutes § 53-202 (c), which provides: "Any person who possesses or uses a machine gun for an offensive or aggressive purpose shall be fined not more than one thousand dollars or imprisoned not less than five years nor more than ten years or be both fined and imprisoned." Subsection (d) of § 53-202 provides in relevant part: "The possession or use of a machine gun shall be presumed to be for an offensive or aggressive purpose . . . (3) when the machine gun is of the kind described in subsection (g) hereof and has not been registered as therein required; or (4) when empty or loaded projectiles of any caliber which have been or are susceptible of use in the machine gun are found in the immediate vicinity thereof." Subsection (e) of § 53-202 provides: "The presence of a machine gun in any room, boat or vehicle shall be presumptive evidence of the possession or use of the machine gun by each person occupying such room, boat or vehicle." Furthermore, subsection (g) of § 53-202 in turn provides in relevant part: "Any person who fails to register any gun as required hereby shall be presumed to possess the same for an offensive or aggressive purpose."

The dispositive issues in this case are: (1) whether the trial court's jury instructions on § 53-202 (d), (e) and (g), providing for mandatory rebuttable presumptions of possession and purpose, violated the due process clause of the federal constitution; and (2) whether the trial court's instructions were harmless error. We conclude that the instructions did violate the due process clause and that the jury instructions were not harmless beyond a reasonable doubt.

The defendant was charged in an amended information with possession of a machine gun for an offensive or aggressive purpose in violation of § 53-202 (c), knowingly having a weapon in a vehicle in violation of General Statutes § 29-38, altering or removing an identification mark on a weapon in violation of General Statutes § 29-36, and reckless endangerment in the first degree in violation of General Statutes § 53a-63 (a). All of these charges arose out of one incident involving the defendant's alleged possession and use of a machine gun. After a jury trial, he was found guilty of possession of a machine gun for an offensive or aggressive purpose, and not guilty of the remaining charges. He was sentenced to five years imprisonment, execution suspended after three years. Following his conviction, the defendant moved for a new trial, raising the dispositive issues before us in this appeal. The trial court denied the motion. The defendant appealed from the judgment of the trial court to the Appellate Court, and we transferred the appeal to this court pursuant to General Statutes § 51-199 (c) and Practice Book § 4023.

The essential facts that the jury could reasonably have found are not in dispute. At approximately 4:35 a.m. on March 7, 1993, Lieutenant Ronald Bussell and Officer Brian Wood of the Darien police department were completing an automobile stop on Hoyt Street in Darien when they heard several rapidly fired gunshots. The officers looked in the direction from which the shots came, heard the sound of a motor vehicle, and then observed a vehicle moving eastbound on Camp Avenue, which intersects with Hoyt Street. The driver of the vehicle turned onto Hoyt Street and drove toward the officers, who signaled for him to pull over. The driver did not stop, and the officers followed in pursuit until they stopped the vehicle approximately one-half mile from where it had first passed them.

The officers approached the vehicle and found the defendant in the front passenger seat and David Caruthers in the driver's seat. They observed that the driver's window was rolled up, while the defendant's window was rolled down. They also noted that Caruthers appeared nervous and that the defendant stared straight ahead, not looking at either of the officers. While Bussell obtained the vehicle's registration and identification from the occupants, Wood noticed a shell casing on the floor behind the defendant's seat. Wood informed Bussell of the casing and Bussell called for backup units. From where he was standing, Bussell was able to see two shell casings on the floor behind the defendant's seat.

The officers removed Caruthers and the defendant from the vehicle and searched both them and the vehicle. As a result of their search of the vehicle, the officers found only the two shell casings. Believing that a gun may have been thrown from the vehicle, the area was canvassed. A machine gun and a magazine were located on the east side of the road that the officers had driven down during the pursuit.

A firearms examiner at the state police forensic laboratory determined that the machine gun, which was not registered to either Caruthers or the defendant, could be switched from automatic to semi-automatic mode. He also determined that the shell casings found in the vehicle had been fired from the gun. He testified that, when the gun was fired, the shells ejected to the right and slightly to the rear.

At the defendant's trial, Caruthers testified that he had pleaded nolo contendere to charges of possession of a machine gun in connection with his arrest with the defendant on March 7, 1993. He stated that he had borrowed the vehicle and picked up the defendant, that he had not placed the gun in the vehicle, and that he had neither shot a gun nor thrown one out of the vehicle that night.

The defendant testified that he had been intoxicated on the night of the arrest and remembered very little. He testified that Caruthers had picked him up at his girlfriend's house on Camp Street and that he had not seen a gun in the vehicle. He stated that the front passenger window was rolled down when he entered Caruthers' vehicle and, although it was cold outside, he had left the window open while he smoked a cigarette and let the cold air revive him. He further testified that he had not seen anyone firing a gun on the night of his arrest. He added that he had strong feelings against the possession of guns, and that he was unfamiliar with their operation.

The trial court instructed the jury that, pursuant to § 53-202, the presence of a machine gun in any vehicle shall be presumptive evidence of possession or use of the gun, and that the failure to register the gun or the presence of any empty or loaded projectiles of any caliber, which have been or are susceptible of use in the machine gun, is presumptive evidence that the gun was possessed for an offensive or aggressive purpose. The trial court further instructed the jury that "[p]resumptive evidence is defined as evidence which must be received and treated as true and sufficient until rebutted by other testimony." The defendant did not challenge those instructions. The state, however, concedes that the constitutionality of these presumptions is reviewable under either the Golding or the plain error doctrine because those mandatory rebuttable presumptions violate the defendant's fundamental constitutional right that the state prove every element of the crime charged beyond a reasonable doubt. Nonetheless, the state argues that the defendant is not entitled to relief because the challenged instructions were harmless beyond a reasonable doubt. We address these issues in turn.

I

It is clear, as conceded by the state, that the trial court's instructions, which included several of the mandatory rebuttable presumptions set forth in § 53-202 regarding inferences of possession and aggressive or offensive purpose, cannot pass constitutional muster. The Supreme Court of the United States in Francis v. Franklin, 471 U.S. 307, 105 S.Ct. 1965, 85 L.Ed.2d 344 (1985), reasoned as follows: "The Due Process Clause of the Fourteenth Amendment protects the accused against conviction except upon proof beyond a reasonable doubt of every fact necessary to constitute the crime with which he is charged. In re Winship, 397 U.S. [358, 364, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970)]. This bedrock, axiomatic and elementary [constitutional] principle . . . prohibits the State from using evidentiary presumptions in a jury charge that have the effect of relieving the State of its burden of persuasion beyond a reasonable doubt of every essential element of a crime. . . . The prohibition protects the fundamental value determination of our society, given voice in Justice Harlan's concurrence in Winship, that it is far worse to convict an innocent man than to let a guilty man go free. . . . The question before the Court in this case is almost identical to that before the Court in Sandstrom [v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979)]: whether the challenged jury instruction had the effect of relieving the State of the burden of proof enunciated in Winship on the critical question of . . . state of mind . . . by creating a mandatory presumption of intent upon proof by the State of other elements of the offense.

"The analysis is straightforward. The threshold inquiry in ascertaining the constitutional analysis applicable to this kind of jury instruction is to determine the nature of the presumption it describes. . . . The court must determine whether the challenged portion of the instruction creates a mandatory presumption . . . or merely a permissive inference . . . . A mandatory presumption instructs the jury that it must infer the presumed fact if the State proves certain predicate facts. A permissive inference suggests to the jury that a possible conclusion may be drawn if the State proves predicate facts, but does not require the jury to draw that conclusion.

"Mandatory presumptions must be measured against the standards of Winship as elucidated in Sandstrom. Such presumptions violate the Due Process Clause if they relieve the State of the burden of persuasion on an element of an offense. Patterson v. New York, [ 432 U.S. 197, 215, 97 S.Ct. 2319, 53 L.Ed.2d 281 (1977)] ([A] State must prove every ingredient of an offense beyond a reasonable doubt and . . . may not shift the burden of proof to the defendant by presuming that ingredient upon proof of the other elements of the offense). . . . A permissive inference does not relieve the State of its burden of persuasion because it still requires the State to convince the jury that the suggested conclusion should be inferred based on the predicate facts proved. Such inferences do not necessarily implicate the concerns of Sandstrom." (Citations omitted; internal quotation marks omitted.) Francis v. Franklin, supra, 471 U.S. 313-14.

Although the state concedes that the trial court incorrectly instructed the jury that the presumptions contained in § 53-202 (d), (e) and (g) were mandatory rebuttable presumptions, it argues that we should construe those presumptions as permissive inferences under appropriate circumstances in order to preserve them in a constitutional manner. We agree.

The United States Supreme Court in Ulster County Court v. Allen, 442 U.S. 140, 157, 99 S.Ct. 2213, 60 L.Ed.2d 777 (1979), noted that a statutory permissive inference is one "which allows . . . the trier of fact to infer the elemental fact from proof by the prosecutor of the basic one and which places no burden of any kind on the defendant. . . . When reviewing this type of device, the Court has required the party challenging it to demonstrate its invalidity as applied to him. . . . Because this permissive presumption leaves the trier of fact free to credit or reject the inference and does not shift the burden of proof, it affects the application of the `beyond a reasonable doubt' standard only if, under the facts of the case, there is no rational way the trier could make the connection permitted by the inference. For only in that situation is there any risk that an explanation of the permissible inference to a jury, or its use by a jury, has caused the presumptively rational factfinder to make an erroneous factual determination." (Citations omitted.) See also Carella v. California, 491 U.S. 263, 265, 109 S.Ct. 2419, 105 L.Ed.2d 218, reh. denied, 492 U.S. 937, 110 S.Ct. 23, 106 L.Ed.2d 636 (1989) (court must determine "whether the specific instruction, both alone and in the context of the overall charge, could have been understood by reasonable jurors to require them to find the presumed fact if the State proves certain predicate facts").

We have the authority to construe our own statutes. State v. Williams, 205 Conn. 456, 473, 534 A.2d 230 (1987). Indeed, "where a statute permits two constructions, one valid and the other invalid as unconstitutional, the valid construction should be adopted, even where it is not the obvious one." Engle v. Personnel Appeal Board, 175 Conn. 127, 134, 394 A.2d 731 (1978); State v. Warren, 169 Conn. 207, 217, 363 A.2d 91 (1975) ("statute cannot be held unconstitutional unless its invalidity is established beyond a reasonable doubt"). Although this court in the past has refused to construe a mandatorily phrased presumption, which permitted possession of a gun to be inferred from the mere fact of the gun's location, as a permissive inference in order to save it; State v. Watson, 165 Conn. 577, 596-97, 345 A.2d 532 (1973), cert. denied, 416 U.S. 960, 94 S.Ct. 1977, 40 L.Ed.2d 311 (1974); we do so now in accordance with the principles discussed previously.

In the present case, to preserve the relevant provisions of § 53-202 as permissive inferences, we must construe "shall" as "may." General Statutes § 53-202 (d), (e) and (g). It is not conceivable that, pursuant to § 53-202 (d)(3), (d)(4) or (g), the legislature intended for a jury to be required to infer that a defendant had possessed a machine gun for an offensive or aggressive purpose from the mere fact that the gun was unregistered or that live ammunition or shell casings were located in the immediate vicinity of the gun. Rather, it is more likely that the legislature intended that a jury may infer such intent if the statutory predicate fact together with additional appropriate facts are sufficient to render the inference rational. Likewise, it is not reasonable to conclude that, pursuant to § 53-202 (e), the legislature intended to require a jury to infer that all occupants of a vehicle possess a machine gun merely because the gun is located in the vehicle. Rather, it is more likely that the legislature intended that a jury may infer possession under appropriate factual circumstances.

Accordingly, we construe these statutory inferences as permissive inferences that a jury may draw under appropriate circumstances in which such an inference is rational or reasonable. "A permissive inference violates the Due Process Clause only if the suggested conclusion is not one that reason and common sense justify in light of the proven facts before the jury. Ulster County Court [v. Allen, supra, 442 U.S. 157-63]." Francis v. Franklin, supra, 471 U.S. 314-15; see also Tot v. United States, 319 U.S. 463, 467-68, 63 S.Ct. 1241, 87 L.Ed.2d 1519 (1943) (due process requires that there be at least a "rational connection between the fact proved and the ultimate fact presumed" that is grounded in "common experience").

The United States Supreme Court in Leary v. United States, 395 U.S. 6, 89 S.Ct. 1532, 23 L.Ed.2d 57 (1969), analyzed a presumption that authorized the jury to infer from the defendant's possession of marijuana two necessary elements of the crime. The Leary court held that "a criminal statutory presumption must be regarded as `irrational' or `arbitrary,' and hence unconstitutional, unless it can at least be said with substantial assurance that the presumed fact is more likely than not to flow from the proved fact on which it is made to depend." Id., 36; see also Ulster County Court v. Allen, supra, 442 U.S. 165 (there must be "a `rational connection' between the basic facts that the prosecution proved and the ultimate fact presumed, and the latter is `more likely than not to flow from' the former").

An inference of possession or intent based solely on the statutory predicate facts enumerated within § 53-202 would not pass constitutional muster. Reason and experience would not permit the drawing of such inferences. If, however, other facts or circumstances are introduced and the totality of the evidence could reasonably and logically support the inference, then the jury may be instructed that it may draw such a permissive inference. In sum, the jury must be instructed that it may infer facts only upon finding sufficient predicate statutory and nonstatutory facts and circumstances that are rationally connected with the ultimate facts inferred. See Ulster County Court v. Allen, supra, 442 U.S. 158-63; State v. Alfonso, 195 Conn. 624, 633-35, 490 A.2d 75 (1985) (insufficient evidence to infer possession of one drug, but sufficient evidence, including additional predicate facts, to allow an inference of possession of another drug).

II

The state, however, argues that the inclusion of the mandatory rebuttable presumptions in the jury instructions was harmless beyond a reasonable doubt. The defendant claims, to the contrary, that the state failed to prove that the inclusion of the mandatory presumptions was harmless beyond a reasonable doubt.

Since Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967), the United States Supreme Court has "repeatedly reaffirmed the principle that an otherwise valid conviction should not be set aside if the reviewing court may confidently say, on the whole record, that the constitutional error was harmless beyond a reasonable doubt." Delaware v. Van Arsdall, 475 U.S. 673, 681, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986); Rose v. Clark, 478 U.S. 570, 576, 106 S.Ct. 3101, 92 L.Ed.2d 460 (1986). "Despite the strong interests that support the harmless-error doctrine, the Court in Chapman recognized that some constitutional errors require reversal without regard to the evidence in the particular case." Rose v. Clark, supra, 577. Errors that are not subject to harmless error analysis go to the fundamental fairness of the trial. The court made it clear in Rose that "if the defendant had counsel and was tried by an impartial adjudicator, there is a strong presumption that any other errors that may have occurred are subject to harmless-error analysis. The thrust of the many constitutional rules governing the conduct of criminal trials is to ensure that those trials lead to fair and correct judgments." Id., 579. The court in Rose held that the harmless error analysis was required for the mens rea element of a crime. Id., 577-78 (harmless error analysis applied to mental state of mind required for murder).

Accordingly, we apply the Chapman test of harmless error analysis to the constitutional violation in this case: whether it appears "beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained." Chapman v. California, supra, 386 U.S. 24. In other words, we review the record to determine whether "there is a reasonable possibility that the evidence [or the mandatory presumptions] complained of might have contributed to the conviction . . . ." (Internal quotation marks omitted.) Yates v. Evatt, 500 U.S. 391, 403, 111 S.Ct. 1884, 114 L.Ed.2d 432 (1991).

In order for the defendant to be convicted under § 53-202 (c), the state must prove that (1) he had possession of the machine gun, and (2) the possession or use was for an offensive or aggressive purpose. As noted previously, the mere fact that the machine gun came from the vehicle in which the defendant was an occupant is not sufficient evidence that the machine gun was in the defendant's possession. See State v. Alfonso, supra, 195 Conn. 633; State v. Watson, supra, 165 Conn. 596-97. While there was some evidence that the machine gun may have been fired by a person sitting in the passenger seat, because of the location of the shell casings in the rear of the vehicle, we cannot conclude with any degree of certainty that the evidence adduced at trial was so overwhelming that it foreclosed the possibility that the jury may have relied upon the improper mandatory presumption regarding possession rather than upon that evidence.

Furthermore, the jury's finding in this case of not guilty on another count charged involving the machine gun implies that the jury would not have found that the defendant had use or possession of the machine gun without the aid of the mandatory rebuttable presumption of possession. The jury found the defendant not guilty of knowingly having a weapon in a vehicle in violation of § 29-38. The weapon at issue was the same machine gun that formed the basis for the state's charge under § 53-202 (c). The trial court's instructions to the jury with respect to § 29-38 did not include a presumption of possession. The jury, however, did find the defendant guilty under § 53-202 (c), where the mandatory rebuttable presumption of possession had been included in the jury instructions. This discrepancy leads us to conclude that the charged presumption of possession pursuant to § 53-202 (e) was instrumental to the jury's finding of guilt. The state therefore has failed to prove that the erroneous instruction on possession was harmless beyond a reasonable doubt.