Ohio Rev. Code § 3513.02
If, in any odd-numbered year, no valid declaration of candidacy is filed for nomination as a candidate of a political party for election to any of the offices to be voted for at the general election to be held in such year, or if the number of persons filing such declarations of candidacy for nominations as candidates of one political party for election to such offices does not exceed, as to any such office, the number of candidates which such political party is entitled to nominate as its candidates for election to such office, then no primary election shall be held for the purpose of nominating party candidates of such party for election to offices to be voted for at such general election and no primary ballots shall be provided for such party. If, however, the only office for which there are more valid declarations of candidacy filed than the number to be nominated by a political party, is the office of councilperson in a ward, a primary election shall be held for such party only in the ward or wards in which there is a contest, and only the names of the candidates for the office of councilperson in such ward shall appear on the primary ballot of such political party.
The election officials whose duty it would have been to provide for and conduct the holding of such primary election, declare the results thereof, and issue certificates of nomination to the persons entitled thereto if such primary election had been held shall declare each of such persons to be nominated as of the date of the ninetieth day before the primary election, issue appropriate certificates of nomination to each of them, and certify their names to the proper election officials, in order that their names may be printed on the official ballots provided for use in the succeeding general election in the same manner as though such primary election had been held and such persons had been nominated at such election.
R.C. § 3513.02