State law may not, but the Volkmer/McClure act signed by President HW Bush says one may own a machine gun if it was manufactured before May 1986 but not after.
So...federal law supersedes state law. The only way you can own a machine gun manufactured after May 1986 is if you are a Class III machine gun dealer or a machine gun manufacturer.
Ed
Amendment Two
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.