N.Y. Mult. Dwell. Law § 356
Any action or proceeding referred to in this article shall be brought in the supreme court, county court or other court of competent jurisdiction in the county in which the premises are situated. At or before the commencement of the action or proceeding the complaint shall be filed in the office of the clerk of the county, together with a notice of the pendency of the action or proceeding, containing the names of the parties, the object of the action or proceeding and a brief description of the premises affected thereby. Said notice shall be recorded immediately by the clerk. The owner or lessee, or both, of said premises may appear in such action or proceeding and answer or move with respect to the complaint, and the subsequent procedure shall be the same as in other actions or proceedings brought to establish a lien or encumbrance upon real property. Such action or proceeding shall be entitled to a preference in the trial or hearing thereof.
N.Y. Mult. Dwell. Law § 356