The first car mounted radio-telephone
A detailed article on the pioneering efforts of the Detroit Police Department with wireless mobile is here:
http://www.detroitnews.com/history/police/police.htm
Police and emergency services drove mobile radio pioneering, therefore, with little thought given to private, individual telephone use. Equipment in all cases was chiefly experimental, with practical systems not implemented until the 1940s, and no interconnection with the the land based telephone system.[FCC: (external link)] Having said this, Bell Laboratories (external link) does claim inventing the first version of a mobile, two way, voice based radio telephone in 1924 and I see nothing that contradicts this, indeed, the photo below from their site certainly seems to confirm it!

http://www.bell-labs.com/history/75/gallery.html
For the difficulty involved in dating radio history, consider this page: http://members.aol.com/jeff560/chrono1.html