Upon the petition of the owner or operator of any railroad, the county board is authorized to vacate such part of a public road, outside of incorporated cities and villages, lying within the right-of-way of such railroad, and not part of a state highway, if it appears that such crossing should be eliminated in the interest of public safety. Such petition shall be filed with the county clerk of the county in which such part of a public road is located. The same procedure shall be followed in the elimination of railroad grade crossings as is provided for the relocation, vacation, and abandonment of public roads as set forth in sections 39-1722 to 39-1725.