Phil,
Federal law and state laws often intersect here in the USA. I'll give you an example of an incident I was involved in around the early 1980's.
I was flying around turning avgas jet into noise late one night. A person in another county committed a grand theft of a small fixed wing aircraft. Not only is it a federal crime but it is a violation of state law. The pilot was also later determined to be under the influence of alcohol and drugs.
After buzzing around southern California he works his way through my jurisdiction. In the process busts the airspace at my home airport and at the same time makes some aggressive maneuvers toward another law enforcement helicopter. Under federal law that would be along he lines of a 'reckless operation." Under state law we would call it assault with a deadly weapon on a police officer, a felony.
The pilot continues on and busts the Class B (we called it a TCA then) at LAX forcing numerous passenger jets to divert. Eventually this guy has had enough fun & decides to land at my home airport. Of course he lands without talking to anyone causing another passenger jet on final to go around.
My question is do we in law enforcement ignore all this just because some federal crimes are involved? Did you know bank robbery is a federal crime? Local police are the first responders. Local police have every right in fact a duty to enforce ALL laws.
As another less extreme example, local law enforcement sees an aircraft land at an airport, less than an hours flying time from the Mexican border, no lights, no communication, should they be suspicious and investigate? Under the law, you have every right to investigate.
In my home state of California, (I'd guess it's the same all over the USA) police officers can enforce all laws when they have probable cause to believe a crime has been committed. It's a simple matter of filing the case in the appropriate court. Violation of state laws is filed in superior court with the district attorneys office. Federal charges are filed in federal court with the US Attorneys office..
Just because a crime may be a federal crime, it doesn't mean the local police have to say "Kings X." Nothing could be further from the truth. It is only under very rare circumstances a police aircrew going to ask or direct you to do anything. If they ask you to land and wait by your aircraft, wait for the nice men in the blue uniforms, my advice would be to comply, not run to the bar down the street & have a few belts. Chances are good that both the people in that law enforcement aircraft are fully sworn police officers with years of training in enforcing the law. The likely know your rights better than you do. In fact they have to.
Bottom line is some common sense, courtesy and cooperation can go a long way toward clearing up an incident. Of course you can ignore my advice, get cocky, get an attitude, tell the officer they cant touch you under federal law and see what happens. My guess is you will not like the results. I hope this answers your question.