Ohio Rev. Code Ann. § 2949.27

If a convicted felon escapes after sentence of death, and is not retaken before the time fixed for his execution, any sheriff may rearrest and commit him to the county jail, and make return thereof to the court in which the sentence was passed. Such court shall again fix the time for execution, which shall be carried into effect as provided in sections 2949.21 to 2949.26, inclusive, of the Revised Code.