Ohio Rev. Code Ann. § 2713.07

The sheriff shall execute the order of arrest mentioned in section 2713.02 of the Revised Code by arresting the defendant, and delivering to him a copy thereof and of the affidavit. If the defendant cannot be found before the return day, the plaintiff may have further orders without other affidavits or bond until the defendant is arrested. An order of arrest shall not be issued to any other than the county in which the action is brought.