The Uniformed Code of Military Justice (UCMJ) only applies to military personnel on or off a base. While on a base a civilian can be detained and arrested if they violate the rules or laws that apply to everyone ie: DO NOT ENTER, AUTHORIZED PERSONNEL ONLY, etc. These crimes would be held in a federal court house, since all crimes committed on a military installation fall under the federal government. Violation of laws (speed limits) would result in you getting a ticket and the military person that signed or vouched for you to enter the base being disciplined. If you are on the base for business, then you will be sent to a district court for fines, etc. So, the answer is generally, yes if the rules are not solely military related.