SAN FRANCISCO—The U.S. Court of Appeals for the Ninth Circuit has left in place a Berkeley city ordinance that forces retailers to inform prospective cellphone buyers that carrying their devices in certain ways can cause exposure to radio-frequency radiation that exceeds federal limits.

CTIA, a wireless industry trade association, had brought on Theodore Olson of Gibson, Dunn & Crutcher to bring a First Amendment challenge to the local law and to argue that federal regulations pre-empt it.

But a divided Ninth Circuit panel on Friday sided with Berkeley, finding that the compelled disclosure was both factually accurate and in line with requirements that the Federal Communications Commission already requires of cellphone makers.