Per ATF page-
If it is a firearm that does not fall under the National Firearms Act (NFA) description, there is no federal registration. However, there may be state or local requirements and you should contact your state or local agencies.
If the firearm is an NFA firearm you must contact:
Bureau of Alcohol, Tobacco, Firearms and Explosives
National Firearms Act Branch
99 New York Avenue NE, Mailstop 6E 403
Washington, DC20226USA
Voice (304) 616-4500
Please note:
1.An individual may only sell/transfer a firearm to an unlicensed resident of his or her state.
2.You cannot transfer/sell a weapon to someone if you believe or have reasonable cause to believe the person is prohibited from receiving or possessing firearm under Federal law.
3.If the above requirements are met, ATF recommends the buyer and seller both keep a bill of sale (a document who sold the firearm, a description of the firearm, and who bought the firearm) so that if the firearm is ever traced, the buyer/seller can provide the information.