N.Y. Real Prop. Acts. Law § 229

§ 229. Liability of tenant holding over after giving notice of\nintention to quit. If a tenant gives notice of his intention to quit the\npremises held by him, and does not accordingly deliver up the possession\nthereof, at the time specified in such notice, he or his personal\nrepresentatives must, so long as he continue in possession, pay to the\nlandlord, his heirs or assigns, double the rent which he should\notherwise have paid, to be recovered at the same time, and in the same\nmanner, as the single rent.\n