N.Y. CVP Law § 4106

§ 4106. Alternate jurors. One or more additional jurors, to be known\nas "alternate jurors", may be drawn upon the request of a party and\nconsent of the court. Such alternate juror or jurors shall be drawn at\nthe same time, from the same source, in the same manner, and have the\nsame qualifications as regular jurors, and be subject to the same\nexaminations and challenges. They shall be seated with, take the oath\nwith, and be treated in the same manner as the regular jurors. After\nfinal submission of the case, the court may, in its discretion, retain\nsuch alternate juror or jurors to ensure availability if needed. At any\ntime, before or after the final submission of the case, if a regular\njuror dies, or becomes ill, or is unable to perform the duties of a\njuror, the court may order that juror discharged and draw the name of an\nalternate, or retained alternate, if any, who shall replace the\ndischarged juror, and be treated as if that juror had been selected as\none of the regular jurors. Once deliberations have begun, the court may\nallow an alternate juror to participate in such deliberations only if a\nregular juror becomes unable to perform the duties of a juror.\n