Ohio Rev. Code Ann. § 1341.07

When the surety in a judgment, who is certified therein to be such, or his personal representative, pays the judgment, or part thereof, to the extent of such payment he shall have all the rights and remedies against the principal debtor that the plaintiff had at the time of such payment. Proceedings to revive the judgment shall be as provided in cases of dormant unpaid judgments, but in the name of such surety or representative. The plaintiff in the original action shall not be liable for costs therein.