Ohio Revised Code Title XXXV. Elections § 3513.23

(A) If an elector voting at a primary election writes in a blank space provided for that purpose on the ballot of one political party under the title of an office for which a nomination is to be made the name of a person other than the persons whose names are printed on the ballot as candidates for the nomination, and if that elector records the vote in the manner provided on the ballot next to the name written, that ballot shall be counted as a vote for the nomination of the person whose name is so written if that person has filed a declaration of intent to be a write-in candidate under section 3513.041 of the Revised Code.

(B) In no event shall a person whose name is written on a primary election ballot be nominated as a candidate for election to an office if the name of no person living on the day of that primary election is printed on the ballot as a candidate for that nomination, unless the total number of votes cast for the person whose name is written on the ballot is not less than that number of petition signatures that would have been required for the printing of the person's name on the primary ballot pursuant to section 3513.05 of the Revised Code.