A New York rental application is a legal document that allows a landlord to review a potential tenant's background information and references. Rental applications are free for landlords with Zillow Rental Manager, so you can easily verify tenants and fill your vacant rentals online.How to fill out the New York Rental Application Form? 1. Gather all required documents and personal information. 2. Standard Rental Application Forms. Download a Printable Rental Application Form PDF. Easy-to-use New York rental application forms. We offer a free Rental Application form that can be completed online and a Printable Rental Application. There are a few ways to fill out a rental application, depending on the landlord or property owner's preference. Applying online is a time-saving solution.