There is no legal situation specifically restricting bullpups but a combination of several other features usually renders most guns prohibited. See here: budsgunshop.com/feeds/state_reg/new_york_restrictions.pdf

http://nyfirearms.com/forums/rifles/104445-rdb-c-kel-tecs-new-ny-legal-bullpup.html#post1203139

Aaron, no Sir. It would have the same restrictions as any other Semi-Auto Rifle : The following are prohibited:✘Semi-automatic rifles that can accept a detachable magazine and have one or more of the following features: 1.Folding / telescoping stock 2.Pistol grip 3.Thumbhole Stock 4.Fore-grip 5.Bayonet lug 6.Flash suppressor 7.Muzzle brake 8.Muzzle compensator 9.Threaded barrel10.Grenade launcher 11.Over 10 round capacity