Ohio Rev. Code Ann. § 2729.19

The costs to be taxed upon an application to restore lost or destroyed records mentioned in section 2729.14 of the Revised Code shall be the same as provided for like services in civil actions. Where the record is lost or destroyed by fire, riot, civil commotion, or other cause, the cost of replacing and restoring it, as provided in sections 2729.14 to 2729.16, inclusive, of the Revised Code, shall be paid out of the county treasury on the order of the court.