No department of the city shall accept, lay out, open, improve, grade, pave, curb, or light any street or other way, unless the street or way:
(A) Shall have been accepted or opened or otherwise shall have received the legal status of a public street or way; or
(B) Unless the street or way corresponds in location and extent with a street or way shown on a recorded plat which shall have been legally accepted by council of the city.
('68 Code, § 28.2)