It depends. Per the Instructions for the NY Form IT-249, the policy must qualify under IRC § 7702B in order to qualify for the Long-Term Care Credit. The law specified states the policy must not have a cash surrender value.
If your insurance policy has a cash surrender value, then you do not qualify for the credit. If you are unsure, your insurance company that issued your policy should be able to tell you if the policy qualifies under IRC § 7702B.