The Department of Transportation or the county board shall, prior to the design or construction of a new bridge or culvert in a new or existing highway or road within its jurisdiction, notify in writing, by first-class mail, the natural resources district in which such bridge or culvert will be located. The natural resources district shall, pursuant to section 39-826.02, determine whether it would be beneficial to the district to have a dam constructed in lieu of the proposed bridge or culvert. If the district shall determine that a dam would be more beneficial, the department or the county board and the natural resources district shall jointly determine the feasibility of constructing a dam to support the road in lieu of a bridge or culvert. If the department or the county board and the natural resources district cannot agree regarding the feasibility of a dam, the decision of the department, in the case of the state highway system, or the county board, in the case of the county road system, shall be controlling.