Ohio Rev. Code § 5924.05: Territorial applicability.

(A) This code applies throughout the state. It also applies to all persons otherwise subject to this code while they are serving outside the state, and while they are going to and returning from such service outside the state, in the same manner and to the same extent as if they were serving inside the state.

(B) Courts-martial and courts of inquiry may be convened and held in units of the organized militia while those units are serving outside the state with the same jurisdiction and powers as to persons subject to this code as if the proceedings were held inside the state, and offenses committed outside the state may be tried and punished either inside or outside the state.