In the US, most States require motorized vessels to be registered, whether Coast Guard Documented or not. I believe some States waive registration if a boat is documented with the USCG (non-motorized or commercial). However, no state requires documenting a vessel with the Coast Guard . . . purely an owner option. My boat is CG Documented, (it is motorized and non-commercial) but the State of RI requires registration as well.
Call the NY Dept of Boat Registration to find out your requirements.