N.Y. Comp. Codes R. & Regs. tit. 22, § 510.12 – Motions.

(a) Unless otherwise directed by a judge of the Court of Appeals by order to show cause, the following procedures shall apply to motions concerning capital appeals. A motion addressed to the Court of Appeals may be made on eight days' notice (personal service), nine days' notice (overnight delivery service) or 13 days' notice (service by mail) (see CPLR 2103). Motions are returnable at Court of Appeals Hall, 20 Eagle Street, Albany, NY 12207-1095, every Monday, whether or not the court is in session. Whenever a Monday is a State holiday, motions are returnable on the next day of that week that is not a State holiday. All motions shall be submitted without oral argument. Unless otherwise permitted by the court or the clerk, the papers in support of a motion must be filed at Court of Appeals Hall no later than noon on the Friday preceding the return date. All responding papers must be served and filed at Court of Appeals Hall on or before the return date of the motion. Proof of service on each party must be filed with any papers submitted on a motion. Filings by facsimile transmission will not be accepted without prior authorization of the clerk. No adjournments are possible other than in those narrow circumstances provided by CPLR 321(c).
(b) Reply papers are not permitted by the court's motion practice. Requests for permission to file papers after the motion return date are governed by section 510.14 of this Part.
1. (1) that the parties are not capable of a full and adequate presentation and that movants could remedy this deficiency;
2. (2) that movants would invite the court's attention to law or arguments which might otherwise escape its consideration; or
3. (3) that amicus curiae briefs would otherwise be of special assistance to the court.
  Proposed briefs amicus curiae shall conform to the requirements set forth in section 510.11(e) of this Part.
  (d) Motion for reargument.
  A motion for reargument of an appeal shall be made on 10 copies of a brief or memorandum, with proof of service of three copies. A motion to reargue a motion may be made on one copy of a brief or memorandum with proof of service of one copy. A motion to reargue an appeal or motion shall state briefly the grounds upon which reargument is sought and the points claimed to have been overlooked or misapprehended by the court, with proper reference to the particular portions of the record and to the authorities relied upon. A motion to reargue may not be based on the assertion for the first time of new points except for extraordinary and compelling reasons. Unless otherwise permitted by the court, the notice of motion shall be served not later than 30 days after the appeal or motion has been decided.
  (e) Other motions.
  Motions other than those seeking amicus curiae relief or reargument may be made on a single set of the moving papers, with proof of service of one copy.
(c) Motion for amicus curiae relief.
A brief amicus curiae may be filed only by leave of the Court of Appeals granted on motion, or upon the court's request. Motions for amicus curiae relief must be noticed to be heard no later than the deadline set forth in the final capital appeal management order. Movant must file one copy of the motion and 15 copies of the proposed brief, with proof of service of three copies on each party. Motions for amicus curiae relief must demonstrate to the court's satisfaction at least one of the following:
(f) Motion papers which do not conform to the requirements of this Part may be rejected by the clerk.