In a non-war zone, the MP roles as in the case of all other US forces are set under the staus of forces agreement.

In a war zone, US forces are also subject to a SOFA, depending on the type of conflict. Tht can range from out right martial law with full powers as in a contabulary on down to more traditional roles.

Not a lawyer and I did not stay in a Holiday Inn Express last night so you need to check much further

Best
Tom