Whenever 60 percent or more of the owners of land contiguous to and crossed by some watercourse or drain desire to have such lands drained or such natural course or drain straightened, altered, widened or deepened, they may petition the county court of the county in which the land is situated for such improvement, describing all property affected thereby and giving the names of the owners thereof. Upon the filing of the petition the county court shall ascertain whether 60 percent or more of the owners of land affected have signed the petition, and if so, shall make a finding to that effect.