N.Y. Jud. Law § 402
A term of the appellate division of the supreme court must be attended by the sheriff of the county in which it is held, his under sheriff, or one of his deputies, each of whom must act under the direction of the court or of the presiding justice. The sheriff of the county must cause the room in which a term of the appellate division is held to be properly heated, ventilated, lighted, and kept comfortably clean and in order. The sheriff must also provide the court with all necessary stationery and minute-books, upon the written requisition of the court or of the justice presiding at the term, and shall defray the necessary expense of telegraphing the day calendar to such county clerks as the court shall direct; also the necessary expense of transmitting printed cases and papers to the reporter; to the various libraries and to the justices of the appellate division. The fees of the sheriff for attending a term of the appellate division and all expenses incurred by a sheriff in obedience to this section must be audited by the comptroller and paid out of the treasury of the state.
N.Y. Jud. Law § 402