A sublease agreement is considered a written document that offers the lessee a chance to pass on the responsibility and rights of tenancy to another person. Under state law, the owner must provide written consent before the primary tenant can "assign" (transfer) the lease to you.Rental Application: 1. In New York State, tenants have a right to sublease their apartments. Most leases require the landlord's written permission. Sublease Agreement: 1. The apartment address. 2. Download our free sublease agreement template to use whenever you need it. It gives you peace of mind when bringing on subtenants. Like several clients, McAdams Law represented, you may wake up one day to find an eviction notice taped to your door, and be in a crisis.