The cost of cleaning out and repairing an assessment drain or a drainage structure constructed by any governmental entity for which no continuing funds for maintenance are available must be assessed pro rata against the lands benefited in the same proportion as the original assessment of the costs in establishing such drain, or in accordance with any reassessment of benefits if there has been a reassessment of benefits under the provisions of section 61-16.1-26. If no assessment for construction costs or reassessment of benefits has been made, the water resource board shall make assessments for the cost of cleaning and repairing such drain or drainage structure constructed by any governmental entity for which no continuing funds for maintenance are available in accordance with the provisions of this chapter for the establishment of a new project. The governing body of any incorporated city, by agreement with the board, is authorized to contribute to the cost of cleaning out, repairing, and maintaining a drain in excess of the amount assessed under this section, and such excess contribution may be expended for such purposes by the board.