The proceedings for imposing of special assessment by the board of trustees shall be, as nearly as may be, according to those for special assessments by the mayor and council under the law governing cities of the first class. If improvements are recommended by the Department of Water, Energy, and Environment and a sanitary drainage district is formed adjacent to a watercourse previously improved above such district pursuant to sections 31-508 and 31-509, the board of trustees shall advertise for bids for the construction of such improvements as are recommended by the department and in accordance with plans recommended by the department.