When any drainage district organized under the provisions of sections 31-401 to 31-408 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 in the manner provided in subsection (1) of section 31-436. When any drainage district is dissolved as authorized in this section, any remaining funds of the district shall be distributed to the counties in which the district is situated in the same proportion as the area of the district in each county bears to the total area of the district, and shall be deposited in the general fund of the respective counties.