After the completion of work in the construction of public improvements as provided in section 16-672.05, the city engineer shall file with the city clerk a certificate of acceptance, which acceptance shall be approved by the mayor and city council by ordinance. The mayor and city council shall then require the city engineer to make a complete statement of all the costs of such improvement and a plat of the property in the storm water sewer district and a schedule of the amount proposed to be assessed against each separate parcel of real property in such district, which shall be filed with the city clerk within ten days from the date of the acceptance of the work. The mayor and city council shall then order the clerk to give notice that the plat and schedules are on file in his or her office and that all objections thereto, or to prior proceedings on account of errors, irregularities, or inequalities, not made in writing and filed with the city clerk within twenty days after the first publication of the notice shall be deemed to have been waived. Such notice shall be given by two publications in a legal newspaper in or of general circulation in the city and by notices posted in three conspicuous places in such storm water sewer district. Such notice shall state the time and place where objections, filed as provided in this section, shall be considered by the mayor and city council.