No lease & landlord is dq in paying common charges

In NYC you are now likely on a month-to-month lease, which began after the original lease term ended. You don't say who sent you this letter, but likely the building has the right to collect delinquent common charges from the rent. You still owe rent, you have a lease and the only question is whether the letter is valid. Who sent you the letter? I would confirm with you current landlord.

In our condo rentals, if we fall behind in our cc's, they have the right to collect rent from our tenants to pay for them. Terms vary of course by condo. As Goldie said, check who sent the letter and call your LL. Also agree that you're most likely on a month to month at this point.

Your original question is whether you can live rent-free because you have no written lease. Common law took care of situations like this by construing month-to-month tenancy. According to section 232 of NYS Real Property Law, which codified the common law, you are a month-to-month tenant. The details of the tenancy depend on whether you live in NYC or outside NYC. The real question is who you have to pay, but that's not the question you asked.