Ohio Revised Code Title XIII. Commercial Transactions § 1341.10

The original sureties of a county officer shall not be released or discharged until the filing of a new bond as required by section 1341.09 of the Revised Code, or the expiration of the time allowed therefor, but shall be liable only for the official acts of such officer from the time of the execution of the original bond to the filing of the second bond, or the expiration of the time allowed therefor.  The cost of the application for release as surety shall be paid by the surety who makes it.