Ohio Rev. Code § 3513.04
Candidates for party nominations to state, district, county, and municipal offices or positions, for which party nominations are provided by law, and for election as members of party controlling committees shall have their names printed on the official primary ballot by filing a declaration of candidacy and paying the fees specified for the office under divisions (A) and (B) of section 3513.10 of the Revised Code, except that the joint candidates for party nomination to the offices of governor and lieutenant governor shall, for the two of them, file one declaration of candidacy. The joint candidates also shall pay the fees specified for the joint candidates under divisions (A) and (B) of section 3513.10 of the Revised Code.
The secretary of state shall not accept for filing the declaration of candidacy of a candidate for party nomination to the office of governor unless the declaration of candidacy also shows a joint candidate for the same party's nomination to the office of lieutenant governor, shall not accept for filing the declaration of candidacy of a candidate for party nomination to the office of lieutenant governor unless the declaration of candidacy also shows a joint candidate for the same party's nomination to the office of governor, and shall not accept for filing a declaration of candidacy that shows a candidate for party nomination to the office of governor or lieutenant governor who, for the same election, has already filed a declaration of candidacy or a declaration of intent to be a write-in candidate, or has become a candidate by the filling of a vacancy under section 3513.30 of the Revised Code for any other state office or any federal or county office.
No person who seeks party nomination for an office or position at a primary election by declaration of candidacy or by declaration of intent to be a write-in candidate and no person who is a first choice for president of candidates seeking election as delegates and alternates to the national conventions of the different major political parties who are chosen by direct vote of the electors as provided in this chapter shall be permitted to become a candidate by nominating petition, including a nominating petition filed under section 3517.012 of the Revised Code, by declaration of intent to be a write-in candidate, or by filling a vacancy under section 3513.31 of the Revised Code at the following general election for any office other than the office of member of the state board of education, office of member of a city, local, or exempted village board of education, office of member of a governing board of an educational service center, or office of township trustee.
R.C. § 3513.04