Ten or more freeholders of any county may petition the board for the erection and construction or acquisition by purchase, gift, or condemnation of any bridge, trestle, or any other structure in the vicinity of their residence, and upon any county road which crosses any stream, body of water, gulch, navigable waters, swamp or other topographical formation constituting a boundary by joining with any other county, city or town, or the state of Washington, or with any other state or with any county, city or town of any other state, setting forth and describing the location proposed for the erection of such bridge, trestle, or other structure, and stating that the same is a public necessity. The petition shall be accompanied by a bond with the same requirements, conditions, and amount and in the same manner as in case of a freeholders' petition for the establishing of a county road. Upon the filing of such petition and bond and being satisfied that the petition has been signed by freeholders residing in the vicinity of such proposed bridge, trestle, or other structure, the board shall direct the county road engineer to report upon the project, dividing any just proportional cost thereof.

In the event two counties or any county and any city or town are petitioned to join in paying for the erection or acquisition of such structure, the board of county commissioners of the counties or the board of county commissioners of the county and governing authorities of the city or town shall act jointly in the selection of the engineer who shall report upon such acquisition or erection.