To possess an "Assault Rifle" in the US you need to have a Type 6 or Type 7 Federal Firearms License. You have to apply to the ATF and the State Department, with a background investigation done by the FBI. You undergo yearly inspections of inventory and records by a federal or designated state agent. The location at which the firearm is stored must be approved at the federal, state, and county level. Pretty much the only people who bother to go through all this are the folks who manufature them for the military.

What most people confusingly label "assault rifles", AR-15s, are not fully automatic or even select fire. Many states even ban you from hunting with them because the cartridges are too small to mortally wound animals with a single shot.

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.

http://en.wikipedia.org/wiki/Assault_rifle#United_States

http://en.wikipedia.org/wiki/Gun_laws_in_New_York

True assault rifles are some of the most difficult things to get your hands on. All automatic (which include burst fire) weapons count as machine guns under the National Firearms Act, and are highly regulated. No machinegun made and registered after 1986 can be legally transferred between civilians. Amongst other difficulties and regulation, that restriction means automatic weapons typically sell for enormous amounts.

The term you're looking for is 'assault weapon' which is a generally poorly defined term. Under the terms of the previous federal assault weapon ban, an assault weapon (rifle) is any weapon that has in addition to detachable magazines (a "clip" in popular culture), has at least two of the following features: a folding or telescoping stock, pistol grip, bayonet mount, flash suppressor, and/or muzzle mounted grenade launcher, as well as AR-15s, TEC-9s, Uzis, and AK-47s - those models being specifically named and banned.

Since we are looking at New York specifically, then the following apply. Rifles and shotguns ("long guns") do not require a state permit for purchase, nor registration, nor a license. Handguns require all three. There are additional restrictions on handguns that will typically limit their licensees to using and carrying them for sport. New York has an assault weapon ban in place, effectively continuing the expired Federal ban.