Whenever any petition presented to either house of the general assembly shall affect the right or interest of any person other than the petitioner, the petition shall be continued to the time as may be ordered by the house in which it is presented, and notice of the pendency of the petition shall be ordered by that house to be served, at the expense of the petitioner, upon the person who shall be interested adversely to the petitioner in it, as by that house shall be deemed reasonable and proper; but if the petitioner shall have served the adverse party with a copy of the petition thirty (30) days before the commencement of the session of the general assembly at which the petition is presented, with a notice of his or her intention to present the petition, and it shall be made to appear to the general assembly that the notice was reasonable and proper, and was properly given, the petition may be considered whenever it is presented; but no petition affecting the interest of any city or town shall be proceeded with at the session at which it shall be presented, unless notice of the petition, in the manner set forth in this section, shall have been served upon the city or town council in open meeting sixty (60) days prior to the presentation of the petition.