Police band radios came in many different configurations. Some operated on multiple channels but one channel at a time. As early as 1907, two-way telegraphy was commercially available but not on a scale that would make police use tractable. Early two-way schemes operated on a simples configuration. Only one station could transmit at a time since all operated on the same radio frequency. The (FRC) Federal Communications Commission assigned only eight radio frequencies for all police departments in America. This was a serious limitation.
This was solved with duplexing. Receivers and transmitters were simply set to different frequencies. Suddenly simultaneous transmission and reception were possible. I've read some early adopters had to use morse code but I've not found anything that collaborates that.
In 1921, Detroit Police Commissioner William P. Rutledge had a radio transmitter installed at police headquarters and in 1922 the FRC, issued a provisional commercial radio license for, 1050 KOP-AM. They had some difficulty maintaining the license as they did not operate continuously. Frequency changed to 1080 in 1925 and was deleted thereafter. More here.
833 WLAW-AM was operated by the NYC police department starting in 1922. It was deleted in 1924. It sent out alerts to police officers. It's primary use was by special radio-equipped motorcycle patrols. The station was managed by M.R. Brennan, superintendent of the NYPD's Telegraph Bureau. More here.
You'll see that most of these share the same frequency. This continued until 1938, when Sheriff Biscailuz debuted a genuine two-way system on 31.90 mc with a callsign of KQBV. More here.
1929 Indianapolis WMDZ 1714 Khz
1930 Berkeley KSW 2410 Khz
1930 Tulare WPDA 1712 Khz
1930 Pasadena KGJX 1712 Khz
1931 Los Angles KGPL 1712 Khz
1931 Omaha KGPI 1714 Khz
1935 San Bernadino KGZY 1712 Khz
???? St. Louis KGPC 1712 Khz
???? Chicago (WPDB, WPDC & WPDD) 1714 Khz
1933 The Bayonne, New Jersey police department successfully operated a two-way system between a central fixed station and radio transceivers installed in police cars; this allowed rapidly directing police response in emergencies. The very high frequency system developed by radio engineer Frank A. Gunther and station operator Vincent J. Doyle. The system operated in “push-to-talk” set up. In 1949 the FCC decreed that all police radio systems were to be limited to that VHF bands.. putting an end to the 4-letter calls.