Ohio Rev. Code § 3515.09
A contest of election shall be commenced by the filing of a petition with the clerk of the appropriate court signed by at least twenty-five voters who voted at the last election for or against a candidate for the office or for or against the issue being contested, or by the defeated candidate for said nomination or election, within fifteen days after the results of any such nomination or election have been ascertained and announced by the proper authority, or if there is a recount, within ten days after the results of the recount of such nomination or election have been ascertained and announced by the proper authority. Such petition shall be verified by the oath of at least two such petitioners, or by the oath of the defeated candidate filing the petition, and shall set forth the grounds for such contest.
Said petition shall be accompanied by a bond with surety to be approved by the clerk of the appropriate court in a sum sufficient, as determined by him, to pay all the costs of the contest. The contestor and the person whose right to the nomination or election to such office is being contested, to be known as the contestee, shall be liable to the officers and witnesses for the costs made by them respectively; but if the results of the nomination or election are confirmed or the petition is dismissed or the prosecution fails, judgment shall be rendered against the contestor for the costs; and if the judgment is against the contestee or if the results of the nomination or election are set aside, the county shall pay the costs as other election expenses are paid.
R.C. §3515.09