Start an eviction proceeding. Your best move will be to hire a landlord-tenant lawyer.
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First, I suggest you retain counsel and not do this yourself. That said, you have not provided enough information.
Assuming it's a holdover and you had the tenant served by a licensed process server with a 30-day notice giving the tenant until the last day of the month following the month in which you served the notice, the next step is to purchase an index number and serve your petition and notice of petition.
Without an attorney representing you, there are many pitfalls and you will most likely spend more money in the long-run, believe it or not.
(1) I may be guessing. Do not act or rely upon this info; (2) We have not established an attorney-client relationship; and (3) If you insist I tell you something upon which you can actually rely: don't eat yellow snow.
Dear Brooklyn Landlord:
If your tenant is a month to month tenant, and there is no rent regulation involved, and you did not serve the termination of tenancy, on your own, and you ended the tenancy on the last day of the month following the month when you gave the notice, the next step, if the tenant does not move out, is commencing a summary holdover proceeding.
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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.