Ohio Revised Code Title XXXV. Elections § 3515.15

The person against whom judgment is rendered in a contest of election may appeal on questions of law, within twenty days, to the supreme court; but such appeal shall not supersede the execution of the judgment of the court. Such appeal takes precedence over all other causes upon the calendar, and shall be set down for hearing and determination at the earliest convenient date. The laws and rules of the court governing appeals apply in the appeal of contested election cases. If the judgment of the lower court is affirmed, the supreme court shall order the judgment of such lower court to be enforced, if the party against whom the judgment is rendered is in possession of the office.