A. On filing a petition signed by a majority of the taxpayers of the county, the board of supervisors may contract for the county with a railroad company for the construction and maintenance of bridges across streams to be used jointly by the railroad company and the public. The board of supervisors shall not contract to pay or be liable to pay more than one-third of the cost of construction and maintenance of a bridge.

B. The petition shall state the total cost of the bridge and the amount to be paid by the county. The board of supervisors shall give notice by publishing the time of the hearing on the petition.