A New York rental application is a legal document that allows a landlord to review a potential tenant's background information and references. Four (4) most recent pay stubs, pension letter, or social security award letter.If self-employed, verified letter from accountant and copy of Schedule C. You may be disqualified if more than one application is received per lottery for your household. You need to provide the source of your income to prove that you can afford the rent. Tax returns and letters of employment would be enough in this regard. 6 months bank statements. New owners are only required to complete this form. • Enter the information on the Direct Deposit form and electronically sign the document. Complete. Property Information.