N.Y. CVP Law § 3106

Rule 3106. Priority of depositions; witnesses; prisoners; designation\nof deponent. (a) Normal priority. After an action is commenced, any\nparty may take the testimony of any person by deposition upon oral or\nwritten questions. Leave of the court, granted on motion, shall be\nobtained if notice of the taking of the deposition of a party is served\nby the plaintiff before that party's time for serving a responsive\npleading has expired.\n (b) Witnesses. Where the person to be examined is not a party or a\nperson who at the time of taking the deposition is an officer, director,\nmember or employee of a party, he shall be served with a subpoena.\nUnless the court orders otherwise, on motion with or without notice,\nsuch subpoena shall be served at least twenty days before the\nexamination. Where a motion for a protective order against such an\nexamination is made, the witness shall be notified by the moving party\nthat the examination is stayed.\n (c) Prisoners. The deposition of a person confined under legal process\nmay be taken only by leave of the court.\n (d) Designation of deponent. A party desiring to take the deposition\nof a particular officer, director, member or employee of a person shall\ninclude in the notice or subpoena served upon such person the identity,\ndescription or title of such individual. Such person shall produce the\nindividual so designated unless they shall have, no later than ten days\nprior to the scheduled deposition, notified the requesting party that\nanother individual would instead be produced and the identity,\ndescription or title of such individual is specified. If timely\nnotification has been so given, such other individual shall instead be\nproduced.\n