Whenever any improvement constructed under this chapter is completed it shall be under the control and supervision of the board of drainage commissioners. But any city or town may convert into a sewer any part of any drain within such corporate limits and to that end may change the location of any such part of such drain on condition only that such change of location or conversion of such drain into a sewer shall not injuriously affect the general purposes of such drainage and that no lands outside of such corporate limits shall be charged thereby with any additional burden.