I'm Lucy, and I'd be happy to answer your questions today.
New York is one of the states that doesn't have specific laws on when a landlord must return a security deposit. As a result, there is unfortunately no provision for double or treble damages like some other states have. The landlord of a property with fewer than 6 units isn't required to put the money into an interest-bearing account. What they are required to do is account for the deposit or return it within a reasonable time. Thirty days is generally considered reasonable.
Failure to return a deposit is not a crime, but the landlord can be sued for breach of contract and required to return it. The reason for them to do it on their own is both to save the time they'd spend going to court and to avoid having to reimburse tenants for their filing fees and post-judgment interest.
Since it's been more than a month and a half and you haven't gotten the deposit back, your recourse is to file a lawsuit against the landlord. These cases are usually brought in Small Claims Court, which is also called the Town and Village Court in some NY counties. The website for your local county court should have forms you can fill out to open a case. They should also have forms in the courthouse if you'd prefer not to have to print them out.
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