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The Alliance military tends to ride to the rescue only when the big guns are needed. For the more mundane crimes, the local sheriffs, Interpol, and the Federal agents are the folk to call.
Just about every town on every planet and moon has some form of local law. In many cases, the law is a man with a tin star looking to keep everyone else in town honest. In others, the law is a bunch of brigands who go around breaking kneecaps on orders from the local governor or magistrate. Whatever form the local law takes, they tend to deal with petty theft and hooligans. When something major comes along – like the assassination of a governor or the kidnapping of a powerful Guild leader – the locals call in either Interpol or the Federal marshals.
Interpol (Interplanetary Police) deals with criminals who have fled the jurisdiction of local law enforcement, as well as crimes committed in areas that are outside local control, though still under Alliance control. (In other words, just about everywhere.) Interpol generally deals more with tracking suspects and investigating interplanetary crime than direct enforcement. The enforcement of federal law and the pursuit of criminals across interplanetary borders falls under the jurisdiction of Federal Marshals.
Federal Marshals (or simply, ‘Feds’) track down wanted criminals and/or bring to trial those who fail to answer a summons. Some Feds are righteous enforcers of the peace, but there are a few who are more bounty hunter than law enforcer and will go after anyone if the money’s good enough. Since they have to travel a far piece to do their jobs, the Feds have a great deal of autonomy. Feds work alone or in teams. They are provided with excellent ships and equipment, though some choose to work undercover if they are on the trail of particularly dangerous (or lucrative) fugitives.