At any time after the sewer or other sanitary system is constructed the governing body of any city lying within the limits of the district may elect to keep and maintain the lateral sewer lying within the city in order and repair and may enter into an agreement with the board to do so.
From the date of the agreement the governing body shall keep the lateral in repair and the board is not required to keep it in order or repair.
After a city elects to keep the lateral sewers within its corporate limits in order and repair the property within the corporate limits of the city shall not be
taxed for running expenses necessary to keep and maintain the lateral sewer lying within the city in order and repair but shall be taxed for the inspection and repairs of the main sewers lying within the city together with the expense of those functions other than sewerage collection within the city performed by the district pursuant to Section 6512 hereof.