When the plans referred to in section 249.360 with reference to subdistricts have been adopted by the board of trustees and the resolution of adoption published as provided therein, the board of trustees shall have the power, when petitioned so to do by a majority of the resident owners of all tracts and parcels of land lying within such subdistrict as laid out in said plans and described in such petition, to provide for the construction of a complete system of lateral sewers in such subdistrict or any part thereof, issue bonds in anticipation of the revenues of such subdistrict in the manner provided in sections 249.390 to 249.420. The board of trustees shall have the power to determine the sufficiency of the petition.