(1) The contract for the work shall specify the portion of the costs to be paid by each fiscal court, and each county shall be severally liable for its proportion. The cost of the work shall be borne in proportion to the total assessed value of each county.
(2) After the completion of the work, the improvement shall be maintained by the fiscal courts or other authorities of the counties or other political divisions joining in the improvements, who shall bear and pay the same proportion of the costs that they severally bore toward the cost of the original improvements.