Ohio Rev. Code Ann. § 2505.16

When a surety upon a supersedeas bond has moved out of the state or is not sufficient, or if the bond is insufficient in form or amount, on motion, the appellate court may order its change or renewal, or that a new supersedeas bond be given, with security to be approved by the court and in an amount to be determined with the limitations specified in section 2505.09 of the Revised Code. If that order is not complied with, the stay of execution shall cease to operate.