N.Y. CPLR 4106
One or more additional jurors, to be known as "alternate jurors", may be drawn upon the request of a party and consent of the court. Such alternate juror or jurors shall be drawn at the same time, from the same source, in the same manner, and have the same qualifications as regular jurors, and be subject to the same examinations and challenges. They shall be seated with, take the oath with, and be treated in the same manner as the regular jurors. After final submission of the case, the court may, in its discretion, retain such alternate juror or jurors to ensure availability if needed. At any time, before or after the final submission of the case, if a regular juror dies, or becomes ill, or is unable to perform the duties of a juror, the court may order that juror discharged and draw the name of an alternate, or retained alternate, if any, who shall replace the discharged juror , and be treated as if that juror had been selected as one of the regular jurors. Once deliberations have begun, the court may allow an alternate juror to participate in such deliberations only if a regular juror becomes unable to perform the duties of a juror.
N.Y. CPLR 4106