N.Y. Ct. Cl. Act § 23
If the amount awarded is deposited, as provided by section twenty-two of this act, any person claiming an interest in the fund may apply to the supreme court in and for the county of Albany, for an order of distribution. Such application shall be made by verified petition setting forth the rights of any and all persons who may have, or claim to have, any interest in or lien or incumbrance on, the property so appropriated and the award therefor, and the names and addresses of such persons, if known. Thereupon, such court shall make an order, describing the property so appropriated, directed to the attorney-general of the state of New York and to all such persons and to any others who may be unknown, who have or claim to have, any right, title, interest, claim or demand in or to said appropriated property or said award, requiring them to appear before such court and to present their claims or demands on account of such appropriation, at a time and place stated in the order, in the city of Albany, not less than thirty days after service of such order, and show cause why a final order of distribution should not be made. If any such persons appear by such petition to be residents of the state of New York, the order shall be served in the same manner as a summons may be served in an action in the supreme court. If the petition states that any are non-residents of the state or that the names or addresses of any are unknown, the order shall require the service of the order by publication as provided by section fourteen of this act. The court may on the return day hear all persons interested and make a final order of distribution or refer any claim to a referee to hear, try and report. The court may likewise on the confirmation of a report of a referee, after eight days' notice to those who appeared on the return day, make a final order of distribution. If all the interested parties are competent and over the age of twenty-one years they may enter into a written stipulation providing for the distribution and the court shall thereupon issue an order which shall implement the stipulation. The determination of the court and final order of distribution shall, unless set aside or reversed on appeal, be final and conclusive upon the owners or other persons claiming any interest in or lien or incumbrance on the property so appropriated and the award therefor.
N.Y. Court of Claims Law § 23