The designation or establishment of a limited access facility shall, by the authority making the designation or establishment, be entered upon the records or minutes of such authority in the customary manner for the keeping of such records or minutes. The state, counties and incorporated cities and towns may provide for the elimination of intersections at grade of limited access facilities with existing state or county roads, and with city or town streets, by grade separation or service road, or by closing off such roads and streets at the right-of-way boundary line of such limited access facility; and after the establishment of any such facility, no highway or street which is not part of said facility, shall intersect the same at grade. No city or town street, county road, or state highway, or any other public or private way, shall be opened into or connect with any such limited access facility without the consent and previous approval of the highway authority of the state, county, incorporated city or town having jurisdiction over such limited access facility. Such consent and approval shall be given only if the public interest shall be served thereby.