Whenever in the progress of the construction of the system of district improvement, it shall become necessary to construct a portion of such system across any public or other road or public utility, the district board shall serve notice in writing upon the public officers, corporation or person having charge of or controlling or owning such road or public utility, as the case may be, of the present necessity of such crossing, giving the location, kind, dimensions and requirement thereof, for the purpose of the system of improvement, and stating a reasonable time, to be fixed by the board, within which plans for such crossing must be filed for approval in case the public officer, corporation or person controlling or owning such road or public utility desire to design and construct such crossing. As soon as convenient, within the time fixed in the notice, the public officers, corporation or person shall, if they desire to construct such crossing, prepare and submit to the board for approval duplicate detailed plans and specifications for such crossing. Upon the return of such approved plans, the public officers, corporation or person controlling such road or public utility shall, within the time fixed by the board, construct such crossing in accordance with the approved plans. In case such public officers, corporation or person controlling or owning such road or public utility shall fail to file plans for such crossing within the time prescribed in the notice, the district board shall proceed with the construction of such crossing in such manner as will cause no unnecessary injury to or interference with such road or public utility. The cost of construction and maintenance of only such crossings or such portion of such cost as would not have been necessary but for the construction of the system of improvement shall be a proper charge against the district, and only the actual cost of such improvement constructed in accordance with the approved plans shall be charged against the district in the case of crossings constructed by others than the district. The amount of costs of construction allowed as a charge against the district shall be credited ratably on the assessments against the property on which the crossing is constructed if chargeable therewith, until the same is fully satisfied.