Ohio Rev. Code § 2941.43: Request for a final disposition on pending charges by prisoner - disposition following trial.

If the convict referred to in section 2941.40 of the Revised Code is acquitted, he shall forthwith returned by the sheriff to the state correctional institution to serve out the remainder of his sentence. If he is sentenced to imprisonment in a state correctional institution, he shall be returned to the state correctional institution by the sheriff to serve his new term. If he is sentenced to death, the death sentence shall be executed as if he were not under sentence of imprisonment in a state correctional institution.