Check your phone book under state government, and look for whatever wildlife management office is listed. They might have a website; most states do. You might start with a websearch of newyork.gov and try your luck.
Your local sheriff's (or equivalent) office could tell you about legalities on LI. Or give you a game warden's phone #. Upstate? Sure, there's a lot of hunting, but I have no idea of NY law...