They are native to New York yes, the eastern grey squirrel is a north american species.¹ However, the squirrels in Central Park, were deliberately introduced.

They are native to New York yes, the eastern grey squirrel is a north american species.¹ However, the squirrels in Central Park, were deliberately introduced. It's unclear whether they were absent from Manhattan naturally, or whether they were extirpated due to urbanization, and the re-introduced later. And about the invasive status of the grey squirrel in Britain, it's sad that they were deliberately released in Britain, because it's not as if they swam across the Atlantic or hopped a freighter. Now you guys are fighting an extermination campaign with all the regrettable suffering it causes to both squirrels and humans. 1: The Urbanization of the Eastern Gray Squirrel in the United States Etienne Benson J Am Hist (2013) 100 (3): 691-710.