In multiple dwellings in New York City and Westchester County, a no-pet lease clause is deemed waived where a tenant "openly and notoriously" kept a pet for at least three months and the owner of the building or his agent had knowledge of this fact. 
NEW YORK CO-OPS and NEW YORK CONDO ASSOCIATIONS MAY HAVE THEIR OWN RULES ON KEEPING PETS. CHECK YOUR LEASE YOUR ASSOCIATION DOCUMENTS.

However, this protection does not apply where the animal causes damage, is a nuisance, or substantially interferes with other tenants. (NYC Admin. Code §27-2009.1(b); Westchester County Laws, Chapter 694). Tenants who are blind or deaf are permitted to have guide dogs regardless of a no-pet clause in their lease. (Civil Rights Law §47)

As always the case, this is subject to interpretation. It is best to get permission in writing from the landlord or property manager.