2017 New York Laws
CPL - Criminal Procedure
Part 2 - The Principal Proceedings
Title J - Prosecution of Indictments in Superior Courts--Plea to Sentence
Article 270 - Jury Trial--Formation and Conduct of Jury
270.35 - Trial Jury; Discharge of Juror; Replacement by Alternate Juror.

270.35 Trial jury; discharge of juror; replacement by alternate juror.
1.  If  at any time after the trial jury has been sworn and before the
  rendition of its verdict, a juror  is  unable  to  continue  serving  by
  reason  of  illness  or  other  incapacity,  or  for any other reason is
  unavailable for continued  service,  or  the  court  finds,  from  facts
  unknown  at  the  time  of  the  selection  of the jury, that a juror is
  grossly unqualified to serve in the case or has engaged in misconduct of
  a substantial nature, but not warranting the declaration of a  mistrial,
  the court must discharge such juror. If an alternate juror or jurors are
  available for service, the court must order that the discharged juror be
  replaced  by  the alternate juror whose name was first drawn and called,
  provided, however, that if the trial jury has begun  its  deliberations,
  the  defendant must consent to such replacement. Such consent must be in
  writing and must be signed by the defendant in person in open  court  in
  the  presence  of the court. If the discharged juror was the foreperson,
  the court shall designate as the new foreperson the juror whose name was
  second drawn and called. If no alternate juror is available,  the  court
  must declare a mistrial pursuant to subdivision three of section 280.10.
2.  (a)  In  determining  pursuant  to this section whether a juror is
  unable to continue serving by reason of illness or other incapacity,  or
  is  for  any  other  reason unavailable for continued service, the court
  shall make  a  reasonably  thorough  inquiry  concerning  such  illness,
  incapacity  or  unavailability, and shall attempt to ascertain when such
  juror will be appearing in court. If such juror fails to appear,  or  if
  the  court  determines that there is no reasonable likelihood such juror
  will be appearing, in court within two hours of  the  time  set  by  the
  court  for  the  trial  to  resume,  the court may presume such juror is
  unavailable for continued service and may discharge such juror.  Nothing
  contained  in  this paragraph shall affect the court's discretion, under
  this or any other provision of law, to discharge a juror who  repeatedly
  fails to appear in court in a timely fashion.
(b)  The  court  shall  afford  the parties an opportunity to be heard
  before discharging a juror. If the court discharges a juror pursuant  to
  this subdivision, it shall place on the record the facts and reasons for
  its  determination  that such juror is ill, incapacitated or unavailable
  for continued service.
(c)  Nothing  contained  in  this   subdivision   shall   affect   the
  requirements  of  subdivision  one  of  this  section  pertaining to the
  discharge of a juror where the trial jury has begun its deliberations.