In cases of districts so lying in more than one (1) county, the board of directors of such districts shall consist of one (1) member from each county, to be appointed by the county court of such county, and the county mayor of each of the counties shall be a member of such board of directors, and the qualifications, powers, and duties of such board of directors shall be the same as provided by parts 6 through 9 of this chapter for boards of directors and members of boards in improvement districts lying entirely in one (1) county.