A New York rental application is a legal document that allows a landlord to review a potential tenant's background information and references. Get information you need to find the best tenants.Learn more about New York rental applications and download our free PDF form. Screen prospective tenants with Avail landlord software. A lot of you have been asking questions on how to rent an apartment in New York City and renting in New York City is just a convoluted topic. A New York rental application is a form that landlords use to screen potential tenants for their rental properties. The way the proposed bill is currently written will obliterate the short term rental market in New York City. 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. This application form is designed for individuals seeking rental housing.