answer:First you have to ask whether the base is on US territory or otherwise. Domestically – you can have three types of jurisdiction – exclusive, joint and proprietary. Exclusive means only the US government has authority. Joint jurisdiction means that both the state and the federal government have jurisdiction. Proprietary means essentially that the federal government does not have territorial jurisdiction over the area – such a buildings leased by a federal agency from a private party and policed by the state. What determines the status is governed by statutes passed in Congress and by the negotiations between federal agencies and and the respective state governors. For military bases, governors enticed by the prospect of economic development, secede state lands to the federal government reserving all, some or none of the jurisdictional rights they had along with that land. So, on some bases, the host state has kept the right to enforce state laws and the jurisdiction is joint, in others, the host state has not reserved any rights (more typically, they will reserve the right to serve process and collect taxes though) and the jurisdiction is exclusively federal. Now – outside of the country – the status of the land upon which a military base is located is governed by international treaty, law and what are known as Status of Forces agreements. You really have to look at the terms of that agreement to find your answer.