(a) whether the notice of hearing was published and posted as required by law, and is otherwise sufficient;

(b) whether all the property and property owners within the proposed district or extension are benefited thereby;

(c) whether all the property and property owners benefited are included within the limits of the proposed district or extension;

(d) whether the establishment or extension of such district is in the public interest. 2. (a) If the town board shall determine that the notice of hearing was not published and posted as required by law or that it is otherwise insufficient, or if it is determined that it is not in the public interest to accomplish the establishment or extension of the district as proposed, the town board shall adopt a resolution stating the reasons for its determination not to establish or extend the district and enter the same in the minutes of its proceedings.

(b) If the town board shall determine that the notice of public hearing was published and posted as required by law and is otherwise sufficient, and that it is in the public interest to establish or extend such district, either in whole or in part, but shall find that any part or portion of the property or property owners within the proposed district or extension are not benefited thereby or that certain property or property owners benefited thereby have not been included therein, the town board shall specify the necessary changes of the boundaries of the proposed district or extension to be made in order that all of the property and property owners and only such property and property owners as are benefited shall be included within such proposed district or extension, 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 and posted in the manner provided in section two hundred nine-d hereof except that such notice shall also specify the manner in which it is proposed to alter the boundaries of the proposed district or extension. Such further hearing shall be conducted in the same manner as the original hearing. 3. If and when the town board shall determine in the affirmative all of the questions set forth in subdivision one of this section, the board may adopt a resolution approving the establishment or extension of the district as the boundaries shall be finally determined and the construction of the improvement or providing of the service therein, which resolution shall be subject to a permissive referendum in the manner provided in article seven of this chapter, except as hereinafter provided. The proposition submitted must be approved by the affirmative vote of a majority of the owners of taxable real property situate in the proposed district or proposed extended district as shown upon the latest completed assessment-roll of the town, voting on such proposition. A petition requesting a referendum shall be sufficient if signed, and acknowledged or proved in the same manner as a deed to be recorded, or authenticated in the manner prescribed by the election law for the authentication of nominating petitions, by the owners of taxable real property situate in the proposed district or proposed extended district, as shown upon the latest completed assessment-roll of said town, in number equal to at least five per cent of the total number of such owners, or by one hundred of such owners, whichever is the lesser. For the purposes of this section, a corporate owner of such taxable real property shall be considered one owner for the purposes of a petition requesting a referendum and shall be entitled to one vote to be cast by an officer or agent of the corporation or other duly authorized person designated by appropriate resolution of such corporation. The town clerk shall cause to be prepared and have available for distribution proper forms for the petition and shall distribute a supply to any person requesting same. 4. (a) If after the expiration of the time for filing a petition requesting that the matter be submitted to a referendum of the property owners of the proposed district or proposed extended district, no such petition has been filed with the town clerk, he shall file a certificate stating such fact in the office of the county clerk and, where the permission of the state comptroller is required for the establishment or extension of a district and the construction of an improvement or the providing of a service therein, in the office of the department of audit and control at Albany, New York.

(b) If such a petition was filed and after the referendum held pursuant to this section, the town clerk shall prepare and file a certificate stating that a petition was filed and a referendum was held pursuant to the provisions of this section and certifying the result of the vote on the proposition submitted at such referendum in the office of the county clerk and, where the permission of the state comptroller is required for the establishment or extension of a district and the construction of an improvement or the providing of a service therein, in the office of the department of audit and control at Albany, New York.