Try making your own New York lease agreement for free here: rental forms
New York state has no limit on security deposits for nonregulated units. However, New York City (among other jurisdictions) with rent controlled/rent stabilized units may have local caps imposed.
New York state requires a security deposit to be kept separate from a landlord’s personal assets, but the statute does not require the deposit to made in a financial institution unless the landlord owns a residential building consisting of at least six units. then he or she must use a financial institution located in New York. (N.Y. Gen. Oblig. Law §§ 7-103 to 7-108).