A New York rental application is a legal document that allows a landlord to review a potential tenant's background information and references. Initial Registration.To register a rental property for the first time, complete and submit the following forms: 1. Where do you fill out a renter's application? There are a few ways to fill out a rental application, depending on the landlord or property owner's preference. How to fill out the New York Rental Application Form? 1. Gather all required documents and personal information. 2. The typical rental application process involves several steps and can vary based on the property and management. Below is a quick overview of the process. Residential Rental Application (Reviewed - October 2021) â–½Download.