Ohio Rev. Code § 3515.02: Application for recount.

If the nomination or the candidacy for election, or the question or issue, concerning which a recount is applied for was submitted only to electors within a county, the application for recount shall be filed within five days after the day upon which the board of elections of such county declares the results of such election.

If the nomination or the candidacy for election, or the question or issue, concerning which a recount is applied for was submitted only to electors of a district comprised of more than one county but less than all of the counties of the state, the application shall be filed within five days after the day upon which the board of the most populous county in such district declares the results of such election.

If the nomination or the candidacy for election, or the question or issue, concerning which a recount is applied for was submitted to electors throughout the entire state, the application shall be filed within five days after the day upon which the secretary of state declares the results of such election.