Tennessee Code Title 58. Military Affairs, Emergencies and Civil Defense § 58-1-113

(a) The governor may order the national guard, or any part thereof, to serve outside the borders of this state or of the United States in order to perform military duty of every description and to participate in parades, reviews, cruises, conferences, encampments, maneuvers or other training and to participate in small arms and other military competitions and to attend service schools.

(b) Officers and enlisted men of the national guard shall be subject to and governed by this chapter while without this state under the order or authorization of the governor under subsection (a) in like manner and to the same extent as when on duty within this state under orders of the governor so as to allow the governor and the courts of this state to have jurisdiction over such guardsmen for offenses committed while physically outside the state, so long as the state where the offense was committed and the accused agree to the trial of the issue in the Tennessee courts.