Whenever the board of trustees shall deem it necessary to make any of the improvements of any road, highway, or street named in section 39-1610, without the filing of the petition referred to in section 39-1611, it shall so determine by resolution of the board. The board shall thereupon publish a notice of the improvements to be made in one or more newspapers having a general circulation in the district once each week during two consecutive weeks. If a majority of the resident owners of land abutting on or adjacent to such road, highway, or street in the district shall file with the clerk of the board of trustees, within twenty days after the first publication of said notice, written objections to the making of said improvements, said improvements shall not be made as provided in said resolution, referred to in section 39-1611, and the resolution shall be repealed. If the objections are not filed against the improvement in the time and manner provided by this section, the board of trustees shall forthwith cause such work to be done or such improvement to be made, contract therefor, and levy assessments, as set forth in sections 39-1623 to 39-1625 to pay the cost thereof.