Any special police district created under the provisions of this chapter may be abolished at the end of any calendar year whenever a majority of the resident landowners therein shall sign a petition directed to the members of the county legislative delegation of the county wherein it is located requesting that the district be abolished, if public notice be given that the petition is to be circulated by three weeks’ publication in some newspaper published in the county and by posting notices thereof in at least three public places within the district. Upon receipt of any such petition the county legislative delegation may pass a resolution directed to the clerk of court and to the county auditor, declaring the district abolished and all the rights and duties thereunder at an end.