In the spirit of "using words correctly", assault rifles are incredibly tightly regulated by the US federal government and various states. Assault rifles are fully automatic weapons (technically select-fire) and have not been legally manufactured for sale since 1986 and require a special federal permit. The rifle used by the person in Connecticut was not an assault rifle, but is categorized as an "assault weapon" by the government (essentially a crippled version of an assault rifle or, as others put it, a scary looking version of a basic semiautomatic rifle).
The short answer is yes, assault rifles are on a separate registry, but NY states appears to essentially ban both assault rifles and assault weapons.