Upon the application of the owner of land included in any plat, and upon proof that all taxes assessed against the land have been paid, and the notice hereinafter provided for given, the district court may vacate or alter all, or any part, of the plat, and adjudge the title to all streets, alleys, and public grounds to be in the persons entitled thereto; but streets or alleys connecting separate plats or lying between blocks or lots or providing access for the public to any public water, shall not be vacated between the lots, blocks, or plats as are not also vacated, unless it appears that the street or alley or part thereof sought to be vacated is useless for the purpose for which it was laid out. If any part of a street, alley, or public ground proposed for vacation terminates at, abuts upon, or is adjacent to any public water, the petitioner shall serve notice of the petition by certified mail upon the commissioner of natural resources at least 60 days before the term at which it shall be heard. The notice under this subdivision creates a right of intervention by the commissioner of natural resources. The petitioner shall cause two weeks published and posted notice of such application to be given, the last publication to be at least ten days before the term at which it shall be heard; and the petitioner shall also serve personally, or cause to be served personally, notice of the application, at least ten days before the term at which the application shall be heard, upon the mayor of the city, the president of the statutory city, or the chair of the town board of the town where the land is situated. The court shall hear all persons owning or occupying land that would be affected by the proposed vacation, and if, in the judgment of the court, the same would be damaged, the court may determine the amount of the damage and direct its payment by the applicant before the vacation or alteration shall take effect. A certified copy of the order of the court shall be filed with the county auditor, and recorded by the county recorder. The district court shall not vacate or alter any street, alley, or public ground dedicated to the public use in or by any plat in any city or town organized under a charter or special law which provides a method of procedure for the vacation of streets and public grounds by the municipal authorities of the city or town.