Ohio Rev. Code § 2301.15
The criminal bailiff shall act for the sheriff in criminal cases and matters of a criminal nature in the court of common pleas and the probate court of the county. Under the direction of the sheriff, he shall be present during trials of criminal cases in those courts and during such trials perform all the duties as are performed by the sheriff. The criminal bailiff shall conduct prisoners to and from the jail of the county and for that purpose shall have access to the jail and to the courtroom, whenever ordered by such courts, and have care and charge of such prisoners when so doing. Under the direction of the sheriff, the criminal bailiff shall convey to state correctional institutions all persons sentenced thereto. He shall receive and collect from the treasurer of state all costs in such criminal cases in the same manner as the sheriff is required to do, and pay the amount so collected to the sheriff of such county.
R.C. §2301.15