Genuine, as in officially issued Handicap Parking Permits are valid just about everywhere including overseas. There are certain things they do not ever allow someone to do like park at a fire hydrant or in a fire zone. Other than that they do let you get away with murder....so to speak. NYC does have something called alternate side parking and I doubt you d get away with parking on the WRONG side however.
I believe the handicap parking permits are nationwide and not limited to just the state they were issued in, unlike driver s permits.