Dear NY laws on landlord's duty to tenant property:
Your question is due to the fact that New York State, is still in many respects, a common law jurisdiction, and the "law" is created by decisions of judges determining controversies. In plain language, that means, New York has chosen not to write laws on some things that are so well understood, that a law will create a new set of problems that no one could foresee. New York unlike many states, lets its landlords and tenants come up with anticipatory language in written leases to deal with many aspects of the landlord and tenant relation. New York courts will enforce a lease, even with harsh terms, as long as a term is not unconscionable and does not violate a statute that specifically voids that term.
So a New York landlord is expected to foresee the day when the tenant is evicted, by court process, the tenant moves voluntarily at the end of the term, the tenant skips out in the middle of night, and for each potential situation make a written agreement about what to do with the personal property of the tenant left behind. A landlord and a tenant may agree that when the tenant moves out at the end of the term ( a planned and not a forced move) that the property left behind is deemed abandoned and may be disposed by the landlord without any liability to the landlord or charge to the tenant.
But when the tenant is evicted by law (in most parts of New York, by a Sheriff, and in New York City by a City Marshal), the tenant will inevitably leave behind personal property, either due to poor planning, or inability to deal with the process ( the reason will not matter), and at the eviction, the Sheriff or City Marshal, will inventory the property and provide duplicate inventories to the landlord and to the tenant. The landlord may arrange for a move out to a storage or warehouse, and must provide the tenant with the location of the property.
If just left behind, our ancient common law tradition makes the landlord an involuntary gratuitous bailee, with the responsibility to take ordinary care of the tenant's property for a reasonable period, while attempting to convince the tenant to move the property on his own.
While the property remains in the landlord's control and possession the landlord even though serving as a bailee without fee and without true consent, may not cause damage to the property by gross neglect and cannot dispose of the property. A landlord may move the property to short term storage as long as the landlord presents all the information to the tenant needed for the tenant to maintain the storage on his own account.
Instead of statutes, New York relies on landlord and tenant to each anticipate the what to do if property is left behind scenario, and come to terms in a written lease, or allow the courtroom made law (the law in the books made by judges deciding cases and controversies) control the event.
For a thorough article on this subject I draw your attention to:
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.