According to the "Movie Guns" website:

"the Smith & Wesson Model 10 snub revolver is the sidearm carried by Sgt. Joe Friday (Jack Webb). In Season 2's "The Shooting Board" (S2E21), Sgt. Friday uses his S&W when confronting a robbery suspect at a laundromat. When asked to give up his weapon for tests, Friday hands it over and the profile of the gun is seen. Friday mentions that it is his Smith & Wesson revolver."

Here's the web page, complete with photos of the episode:
Dragnet (1967) - imfdb :. guns in movies :. movie guns :. the internet movie firearms database

Looks like the bad guy was carrying a New Service!