IMPORTANT: Please only submit ONE application per household. Be advised that if multiple applications are received, only the first one will.Your rental application is your opportunity to stand out amongst other applicants, so pay attention to spelling and grammar. Housing Court Forms. A New York rental application is a legal document that allows a landlord to review a potential tenant's background information and references. Completely fill out each blank and sign where indicated. Download the New York Rental Application Form for free in PDF format.