N.Y. Rapid Trans. Law § 65
The court, after hearing such testimony and considering such proofs as may be offered, shall ascertain and estimate the compensation which ought justly to be made by the city to the respective owners of or persons interested in the property so acquired or extinguished by such proceeding for the improvement and shall instruct the corporation counsel to prepare a transcript of its estimate of damage. Such transcript of estimate shall be accompanied by the third set of maps or plans and memoranda referred to in section fifty-four of this chapter and therein denominated the third set, or a copy thereof, and shall refer to the numbers thereon and shall state the several sums respectively estimated for each of such parcels with the names of the owners or persons interested therein as far as ascertained, together with all of the affidavits and proofs upon which the same are based. Such transcript shall be signed by the justice trying the proceeding and filed with the clerk of the county in which the property affected by the proceeding is situated and when so filed shall constitute the tentative decree of the court. Upon the filing of the tentative decree, the corporation counsel shall give notice by publication twice a week for two weeks in two public newspapers published in such city of the filing of such tentative decree and that the city and any person whose rights may be affected thereby and who may object thereto, or any part thereof, may, on or before a day to be specified in such notice subsequent to the last publication thereof, set forth his objections thereto in writing, duly verified in the manner required by law for the verifiation of pleadings in an action, setting forth the property owned by the objector and his post-office address, and file the same with such clerk. The notice shall also state that the corporation counsel on the date specified therein will apply to the justice who made the tentative decree to fix a time when he will hear the parties so objecting. Every party so objecting, or his attorney, within the same time, shall serve on the corporation counsel a copy of such verified objections. Upon such application the justice shall fix the time when he will hear the parties so objecting and desiring to be heard. At the time so fixed the justice shall hear each person who has objected to the tentative decree and who may then and there appear and shall have the power to adjourn from time to time until all persons who have filed objections and desire to be heard shall be fully heard.
N.Y. Rapid Trans. Law § 65