Bureau of Alcohol, Drugs, Tobacco, Firearms, and Lasers

In the USA before the War BADTFL offices were responsible for issuing of special permit for Combat Armors civilian use, because this kind of equipment was destinated for military and police use.

Chris Taylor mentioned BATF, that was explained as Bureau of Alcohol, Tobacco, Firearms and Explosives at 10mm article (its standard ammo was 10 mm caliber, while the military was into energy weapons).

In real world to curb the illegal use of firearms and enforce the Federal firearms laws, Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) issues firearms licenses and conducts firearms licensee qualification and compliance inspections.

Sources:
 * Fallout manual