Who can own automatic weapons?

Is this based on state law? I had heard that it is illegal for anyone to own except military or law enforcement. Is this true and if so what law covers this?

Automatic regulations are primarily regulated by the national 1934 National Firearms Act. Most states have their own laws as well and it is virtually impossible for a private owner to own machine guns in some states. In other states, it presents various degrees of difficulty for private citizens to own them. However, many people outside of law enforcement own them although it isn’t exactly commonplace,

My father is a firearms dealer and we had several machine guns (Uzis, Mach 10, fully auto AR-15, and a Bullpup) when I was growing up.

Federal firearms dealers licence holders can, or can get an endorsement to own full auto.

http://www.atf.treas.gov/firearms/nlc/ffl/ffl_types.htm

more info there

I have no doubt you will soon get definitive answers to your question.

The general answer is, that for certain specified devices, any non-felon can own them upon passing certain qualifications and paying a “transfer tax” for them.

States, however, can further restrict what can be owned by whom.

It just depends.

Well, we have these folks. In 2000, there were over 1300 registered machine guns in Alaska.

Fully-automatic and selective fire weapons are Class III weapons:

Class III Weapon Requirements.

Owning them is one thing: actually moving them around and firing them is entirely another. Owning them also apparently gives the ATF carte blanche in search and seizure in your home.