Yes, in many states full-auto or select fire firearms are legal. They are covered under NFA.
Originally Posted by atf.gov above
Q: The types of firearms that must be registered in the National Firearm Registration and Transfer Record are defined in the NFA and 27 CFR, Part 479. What are some examples?
Some examples of the types of firearms that must be registered are:
The frames or receivers of machine guns;
Any combination of parts designed and intended for use in converting weapons into machine guns;
Any part designed and intended solely and exclusively for converting a weapon into a machine gun;
Any combination of parts from which a machine gun can be assembled if the parts are in the possession or under the control of a person;Silencers and any part designed and intended for fabricating a silencer;
Destructive devices; and,
“Any other weapon.”
The issue is, is that the registry for full-auto and select fire firearms is closed now. Also there is a lengthy process (imo, others will disagree) in which to purchase them. That's the short version. If you would like to know more please feel free to ask a more specific question.