Please call the ATF and US Customs to verify this information and get the appropriate forms.
ATF
- Firearms and Explosives Imports Branch - Phone: 202-927-8320
US Customs Service - Call the port of entry and ask for a Customs Inspector
From some of the research I have done it looks like regardless if you are a US citizen or a Non-US citizen, if you want to get a firearm through customs you need to fill out the ATF Form 6. And the ATF Branch that takes care of it is the Firearms and Explosives Imports Branch
Bureau of Alcohol, Tobacco & Firearms (ATF)
ATF Online - Firearms and Explosives Imports Branch