I'm not an expert on the topic, but regarding the two former (and one recent) German countries I can refer you to two famous TV shows, the West-German Tatort (Crime Scene) and the East-German Polizeiruf 110 (Police call 110), which are comparable quite well. The answer is mostly based on both Wikipedia sites, since I don't have too much experience with them (not to say with their pre-'90 versions):
Tatort: This was created in 1970 as a police-based crime TV show, broadcast in 90 minute TV-movies. The show has been (and still is) an iconic still running show, with many shows produced a year (and its broadcast on sunday's primetime being unwritten law) and various different detecives from many German cities usually produced by the regional departments of the public (state-funded) television. But I'm not sure how much it classifies as a police procedural, since it more or less concentrates on the work of the police detectives solving the crime (usually a murder), like a classical crime show, not so much on paper and lawyer work (like, say the 50-50 emphasise of Law and Order), and also includes aspects of the detective's personal lifes and problems (though to a small extent).
Polizeiruf 110: As a, say counter-measure, East-Germany started a likewise iconic TV-show in 1971 being on the surface kind of a Tatort-copy. But they kept it more factual, concentrating on the police work and leaving out the personal lifes and problems of the detectives. In this way it probably classifies more for a police procedural. It has to be said, that while being a totalitarian socialist country, the actual law and police system still wasn't that much different from the "Western" countries in its essence, I think. But being a state-produced show (like the Tatort, but in the West there wasn't so much content-control of the public TV by the government) they indeed put some pedagogical effort in it, with the criminals often being depicted as "failed existences" that don't integrate well into the society. And they also didn't concentrate that much on murder, but other (less heavy) crimes (maybe not to show that the GDR has to fight with murder, too). As Wikepedia says:
The scriptwriters attached particular importance to representation of
the criminal and his state of mind, as well as the context of the
crime. Many episodes aimed to teach and enlighten the audience about
what does and what doesn't constitute appropriate behaviour and
appropriate thought, rather than just to entertain. Polizeiruf was one
of the few broadcasts by GDR media in which the real problems and
difficulties of the supposedly more advanced socialist society could
be displayed and discussed to some extent, albeit in a fictionalized
and pedagogicalized environment.
After the reunion in 1990 and till today those two iconic programmes still exist on their own, but with the Eastern Polizeiruf having converged more to the Western Tatort in its structure and content, not so much to a blend of both shows. But this reflects the general political situation of the reunion, which wasn't so much a blend of both cultures, but an annexation of East-Germany by West-Germany. There are now both shows set in cities all over Germany, but with the Polizeiruf still having more shows set in former GDR-states, though being not as famous as the Tatort. And I guess today the Tatort maybe classifies a bit less as police procedural, as the personal lifes of the detectives still play a role and certain Tatort s (like the one from Münster) also feature other entertaining aspects (the funny interaction between the forensic doctor and the detective being quite iconic) generating interrest apart from the crime story itself. But it nevertheless stays a major iconic show delivering high quality crime stories, that also often feature current political and social problems and IMHO give a good objective insight into actual police work (though not being an expert on the topic).
EDIT: As a more referential side note not contributing that much to the analysis part of the question, there has also been a famous precursor to Tatort in West-Germany, Stahlnetz (Steel net), produced from 1958 to 1968. But compared to the later Tatort this was more factual and documentary in nature and concentrating on the police work with objective meticulousness, leaving out any background about the detectives and psychological motives of the criminals. And the cases were based on real cases. The German Wikipedia article (there is no real English one) also says that it was based on the US show Dragnet, which I for myself don't know.