Ohio Rev. Code § 2329.57: Execution issued to another county may be returned by mail.

When execution is issued in a county and directed to the sheriff or coroner of another county, the sheriff or coroner having the execution, after discharging all the duties required of him, may transmit it by mail to the clerk of the court who issued the writ. On proof by such sheriff or coroner that it was mailed soon enough to reach the office where it was issued within the time prescribed by law, he shall not be liable to amercement or penalty if it does not reach the office in due time.