A New York rental application is a legal document that allows a landlord to review a potential tenant's background information and references. Here's a look at everything you need to apply for an apartment, the forms required for the application process, and tips to help ensure you'll get approved.In most cases, the rental application process is relatively straightforward. It should take somewhere from 24 to 72 hours. Simple rental application form for residential use in both PDF and Word document formats. Our templates are both fillable and printable. Download this free Rental Application Form to occupy a rental property from a landlord. Follow these 5 steps to registering your rental property with the city of Phoenix and lets start building passive income! 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.