You can find a basic pet surrender form at If an animal is microchipped, you'll need to contact the microchip company and have the owner information updated; perhaps this is something that could be added to the form (e.g., Is the animal microchipped? If so, please provide chip ID and contact information for the microchip company... ).

We recommend that a legal professional review the form prior to its use, in case other elements are required by the State of New York to ensure a binding agreement. Such elements may include notarization, witness signature(s), complete contact information for the new owner, any applicable general provisions, etc.