Ohio Rev. Code § 2949.24
Unless a suspension of execution is ordered by the court of appeals in which the cause is pending on appeal or the supreme court for a case in which a sentence of death is imposed for an offense committed before January 1, 1995, or by the supreme court for a case in which a sentence of death is imposed for an offense committed on or after January 1, 1995, or is ordered by two judges or four justices of that court, the warden or another person selected by the director of rehabilitation and correction shall proceed at the time and place named in the warrant to ensure that the death sentence of the prisoner under death sentence is executed in accordance with section 2949.22 of the Revised Code. The warden shall make the return to the clerk of the court of common pleas of the county immediately from which the prisoner was sentenced of the manner of the execution of the warrant. The clerk shall record the warrant and the return in the records of the case.
R.C. §2949.24