http://onlinedocs.andersonpublishing.com/oh/lpExt.dll?f=templates&fn=main-h.htm&cp=PORC§ 3515.01. Persons eligible to apply for recount.
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 position 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.
§ 3515.08. Contest of election.
The nomination or election of any person to any public office or party position or the approval or rejection of any issue or question, submitted to the voters, may be contested by qualified electors of the state or a political subdivision.
In the case of an office to be filled or an issue to be determined by the voters of the entire state, or for the offices of members of congress, or for judicial offices higher than that of court of common pleas, or for an office to be filled or an issue to be determined by the voters of a district larger than a county, said contest shall be heard and determined by the chief justice of the supreme court or a justice of the supreme court assigned for that purpose by the chief justice; except that in a contest for the office of chief justice of the supreme court, such contest shall be heard by a justice of such court designated by the governor.
In the case of all other offices or issues, except judicial offices, such contests shall be heard and determined by a judge of the court of common pleas of the county in which the contest arose. In the case of a contest for a judicial office within a county, such contest shall be heard by the court of appeals of the district in which such county is located. If any contestant alleges prejudice on the part of the judges of the court of appeals or the court of common pleas, assigned to hear such appeal, then the chief justice of the supreme court, upon application of any such contestants and for good cause shown, may assign judges from another court to hear such contest.