When any drainage district organized under the provisions of sections 31-301 to 31-305 is comprised of territory located in more than one county and is inactive for a period of at least five years, as determined by resolution of the county board of the county in which such district was organized, the county board may initiate action for dissolution of the district by filing a copy of its resolution with the clerk of the district court of the county in which the original petition for incorporation of such district was filed. After the filing of such resolution, the procedure for dissolution and distribution of any remaining funds shall be the same as that provided in section 31-375.