N.Y. Comp. Codes R. & Regs. tit. 22, § 218.4
(a) Upon appeal from a judgment including a sentence of death (CPL 460.40[1]).
The taking of an appeal by a defendant directly to the Court of Appeals from a superior court judgment including a sentence of death stays the execution of such sentence until determination of the appeal.
(b) Initial CPL article 440 proceedings (CPL 460.40[3]).
Upon motion to the superior court judge or justice who signed the warrant of execution, a defendant sentenced to death shall be granted a stay of execution of a death warrant issued pursuant to Correction Law, article 22-B to allow the defendant an opportunity to prepare and timely file an initial motion in superior court pursuant to CPL 440.10 or 440.20. The order staying execution shall provide that the stay of execution shall continue until (1) the time for taking an appeal to the Court of Appeals from the superior court's denial of such CPL article 440 motion has expired, or (2) if an appeal is taken, until the Court of Appeals determines the appeal.
(c) Subsequent CPL article 440 proceedings (CPL 460.40[3]).