Ohio Rev. Code Ann. § 5924.140

In the organized militia not in federal service, the processes and sentences of its courts-martial shall be executed by the civil officers prescribed by the laws of the state. Where no provision is made for executing those processes and sentences, the process or sentence shall be executed by a United States marshal or deputy marshal, who shall make a return to the military officer issuing the process or the court imposing the sentence, pursuant to Title 32, Section 333, USCA.