My question involves landlord-tenant law in the State of: New York

Hello all, I am a landlord seeking accurate advice on month to month leasing situations and would appreciate any help please.

To begin with, the tenant on our 2nd floor legal 2-family home had a one year lease, after the year had expired it was never renewed. One RE guy is telling me that we are now automatically under month to month leasing rules, is this true or false please? Thanks.