>>7488426
You can not try civillians with UCMJ and try them with out martial law.
When military police take the actions that would otherwise look like an arrest, they are actually apprehending the person. The arrest, if one follows (and it usually does) is performed by a commissioned officer, usually the provost marshal (military equivalent to the chief of police) or a deputy.
A civilian who was apprehended would be held for a civil authority. Ideally, this would be the FBI, but in some cases a local law enforcement agency might have an agreement established with the military post, or they might act at the direction of the FBI.
An analogous example was when a man was accused of exposing himself to a child while on board a cross-country airline flight that terminated in Reno. The cabin crew requested that the FBI respond, but in the meantime, the airport security folks (the airport did not have a police department at that time) took him into custody. The FBI requested that the city police respond, which was how I got involved. The special agent who responded to the airport with a copy of the relevant chapter of the U.S. Code (the local FBI office was conveniently located across the street from the airport) looked up the statute for the charge, begged a probable cause form off of me, and filled it in. He then asked that I transport Mr. Freewilly to the local jail, where he or one of his FBI brethren would take up the case the next day.
Had Mr. F. done the deed on a military post, this might have worked in a similar way.
Law enforcement agencies at different levels of government fight like cats and dogs in the movies and on TV. In real life, they tend to get along well and assist one another all the time.