N.Y. Town Law § 191
Except as otherwise provided in the case of a water storage and distribution district, water quality treatment district or sewage disposal district, a petition for the establishment or the extension of an improvement district shall be signed by the owners of taxable real property situate in the proposed district or extension thereof, owning in the aggregate at least one-half of the assessed valuation of all the taxable real property of the proposed district or extension thereof, as shown upon the latest completed assessment-roll of said town; provided, however, that if there be any resident owners, the petition shall include the signatures of resident owners owning taxable real property aggregating at least one-half of the assessed valuation of all the taxable real property of the proposed district or extension owned by resident owners, according to the latest completed assessment-roll. If a portion only of a parcel of such real estate appearing upon the assessment-roll is situate within the proposed district or extension thereof, then the town board may determine the relative value of the part thereof within the proposed district or extension thereof, based upon the valuation of the entire parcel as the same appears upon the assessment-roll. Such petition shall describe the boundaries of the proposed district or extension in a manner sufficient to identify the lands included therein as in a deed of conveyance, and shall be signed by the petitioners, and acknowledged or proved in the same manner as a deed to be recorded, or authenticated in the manner provided by the election law for the authentication of nominating petitions. If such petition shall request the construction or acquisition of an improvement, it shall state the maximum amount proposed to be expended therefor. If the petition shall not request the construction or acquisition of an improvement but shall propose the performance or supplying of certain services, it may state the maximum amount to be expended annually for such services. In addition, a petition for the establishment or extension of a park or public parking district shall describe the property proposed to be acquired for the purposes thereof.
N.Y. Town Law § 191