Ohio Rev. Code Ann. § 2949.10

An execution under section 2949.09 of the Revised Code may issue to the sheriff of any county in which the defendant resides, is found, or has property, and the sheriff shall execute the writ. If the defendant is taken, the sheriff shall commit him to the jail of the county in which the writ issued and deliver a certified copy of the writ to the sheriff of such county, who shall detain the offender until he is discharged as provided in such section.