(a) The mayor and council or other governing bodies of incorporated municipalities in this state have the exclusive power and authority to establish or authorize the establishment of ferries on rivers which in whole or in part constitute the dividing line between two counties in this state at points touching such incorporated municipalities and to regulate the same.
(b) In all cases where the river is the dividing line between two counties and where the boundaries of any incorporated municipality border upon such river and at a public road crossing, the power and authority to establish a ferry across said river at such public road crossing is hereby vested exclusively in such municipality.