In any county wherein a drainage ditch has been constructed under the provisions of sections 31-101 to 31-134, or by any drainage district which shall have been dissolved, which benefits an area in part within or adjacent to the boundaries of a drainage district organized under Chapter 31, article 3 or 4, a petition may be filed with the county clerk, signed by at least three of the land owners within the district or the proposed district, praying that the county board cause such ditch to be transferred so as to become a part of and operated and maintained in the same manner as the ditch or ditches of a drainage district created under the provisions of Chapter 31, article 3 or 4. Such petition must bear the approval of a majority of the board of directors of such drainage district to which it is to be attached.