When it is desired to improve a secondary road on a county line, as a secondary road assessment district project, the board of supervisors of any county may establish an assessment district in its county, and levy and collect special assessments for the payment of that portion of the estimated cost of the project assessable against lands in that county. Each county shall pay its share of the cost of the project as provided in this chapter, in the same manner as though the project were located wholly within that county.