N.Y. County Law § 256
Upon the evidence presented at the public hearing, and after due consideration of the maps and plans, reports, recommendations and other data filed with it, the board of supervisors shall determine, by resolution, whether or not the proposed facilities are satisfactory and sufficient and, if it shall determine such question in the negative, it shall remand the proceedings to the agency for further study. The agency shall make such further study and amend and revise the maps and plans (including the zones of assessment and allocation of costs if the maps and plans provide therefor) in conformance with its findings, and shall make a further report to the board of supervisors in the same manner as hereinbefore provided. If the revised maps and plans call for an increase in the estimated maximum expenditure for the project, alter the boundaries of the proposed district, or if the maps and plans provide for zones of assessment and allocation of the cost of the facilities, alter the boundaries of the proposed zones of assessment or change the allocation or the costs of the facilities as between the zones of assessment, the board of supervisors shall call a further public hearing thereon in the manner provided in section two hundred fifty-four. When the board of supervisors shall find that the proposed facilities are adequate and appropriate, it shall further determine by resolution,
If the board of supervisors shall determine that it is in the public interest to establish the district, but shall find that (1) any part or portion of the property or property owners within the proposed district are not benefited thereby or (2) that certain property owners benefited thereby have not been included therein, or (3), if zones of assessment are proposed to be established and the costs of facilities allocated among said zones of assessment, that any part or portion of the property or property owners within a proposed zone of assessment should be placed in a different zone of assessment or that a different allocation of the cost should be made as between the zones of assessment, the board shall specify the necessary changes of the boundaries of the proposed district or the necessary changes of the boundaries of any proposed zone of assessment or the necessary changes as to the allocation of costs, as the case may be, to be made in order that all of the property and property owners and only such property owners as are benefited shall be included within such proposed district, or in order that such zones of assessment and the allocation of the costs of the facilities thereto shall represent as nearly as may be the proportionate amount of benefit which the several lots and parcels of land situate in such zones will derive therefrom, and the board shall call a further hearing at a definite place and time not less than fifteen nor more than twenty-five days after such determination. Notice of such further hearing shall be published in the manner provided in section two hundred fifty-four, except that such notice shall also specify the manner in which it is proposed to alter the boundaries of the proposed district, or the boundaries of the zones of assessment or the allocation of the costs of the facilities as between said zones of assessment, as the case may be. If and when the board shall determine in the affirmative all of the questions set forth above, the board may adopt a resolution approving the establishment of the district, as the boundaries shall be finally determined, and the construction of the improvement, and if zones of assessment have been established and an allocation of the costs of the facilities made as between such zones of assessment, further approving the establishment of the initial zones of assessment and the initial allocation of the costs of the facilities as between said zones of assessment. Such resolution shall be subject to permissive referendum as hereinafter provided, except in the case of a water quality treatment district and except in the county of Suffolk. In the county of Suffolk, if the owner or owners of all of the land within the proposed district consent in writing to the formation of the proposed district and the board of elections certify that on or after the date of the first publication of the notice of public hearing hereinabove referred to, there is no registered voter within the proposed district, then and in that case the resolution adopted by the board approving the establishment of a district shall not be subject to referendum, permissive, or otherwise.
N.Y. County Law § 256