When public improvements are made upon a street or part thereof and there are lots or grounds belonging to a city of the metropolitan class but held or used as a part of any utility system or plant owned by such city, either abutting upon or adjacent to such street or embraced within any improvement district, such property shall not be subject to special assessments for the costs of the improvement, but the costs of improving one-half, or such parts of the costs as might otherwise be assessed against such property, shall be paid out of the water fund, gas fund, or other fund available for such purpose and created to pay the costs of operation of such utility. The board or body having charge of such fund is directed to pay such costs of such improvement upon the completion of such improvement to the city treasurer, and the amount so paid shall be applied to pay the partial costs of such improvement. Whenever any water main is laid by a metropolitan utilities district in a street of a city of the metropolitan class and there are lots or grounds abutting upon such street or embraced within any improvement district which are owned and controlled by the city, one-half the cost of constructing such water main in front of such lot or grounds, if special benefits equal such an amount, to be determined by the metropolitan utilities district, but not to exceed fifty cents per lineal front foot, shall be paid out of the general fund of the city. The city council shall provide for the payment of such costs to the metropolitan utilities district.