Ohio Rev. Code § 3515.01
Any person for whom votes were cast in a primary election for nomination as a candidate for election to an office who was not declared nominated may file with the board of elections of a county a written application for a recount of the votes cast at such primary election in any precinct in such county for all persons for whom votes were cast in such precinct for such nomination.
Any person who was a candidate at a general, special, or primary election for election to an office or postion who was not declared elected may file with the board of a county a written application for a recount of the votes cast at such election in any precinct in such county for all candidates for election to such office or position.
Any group of five or more qualified electors may file with the board of a county a written application for a recount of the votes cast at an election in any precinct in such county upon any question or issue, provided that the members of such group shall state in such application either that they voted "Yes" or in favor of such question or issue and that such question or issue was declared defeated or rejected, or that they voted "No" or against such question or issue and that such question or issue was declared carried or adopted. Such group of electors shall, in such application, designate one of the members of the group as chairman, and shall indicate therein the voting residence of each member of such group. In all such applications the person designated as chairman is the applicant for the purposes of sections 3515.01 to 3515.07 of the Revised Code, and all notices required by section 3515.03 of the Revised Code to be given to an applicant for a recount shall be given to such person.
In the recount of absentee ballots that are tallied by county instead of by precinct, as provided in section 3509.06 of the Revised Code, the county shall be considered a separate precinct for purposes of recounting such absentee ballots.
R.C. § 3515.01