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.

Answer in progress

Police Procedural and Crime Drama in Soviet Union and Russia

Contemporary Setting

One of the most popular police procedurals of the Soviet era was ????????? ????? ??????? or Investigation Held by ZnaToKi (ZnaToKi is a word play where it is an acronym consisting of first syllables of the last names of the heroes, and the word itself means “experts”) wich was a series of TV films (cases) from 1971 to 1989 (with another two films added in 2002 and 2003 featuring two of the three aged actors). This would be one closest to the description of police procedural with emphasis on gathering evidence and forensic work.

Speaking of evolution, Leonid Kanevskij — one of the lead actors from those films — hosted a documentary series in recent years called ????????? ????… (Investigation was held by…, as the reference to the Soviet series) which focused on real investigations of famous crimes in Soviet Union from 1917 to 1991.

Historical Setting

Most popular historical periods for setting police detective stories in Soviet Union are tumultuous years during and immediately after major conflicts such as World Wars, Revolution of 1917 and subsequent Russian Civil War. These settings provide ample opportunity for more action-oriented films following the exploits of the tough lawmen who were often veterans of preceding military confrontation.

Two of the most notable films would be 1979 5-part mini-series ????? ??????? ???????? ?????? (The Meeting Place Cannot Be Changed), and 2007 14-episode TV-series ?????????? (Liquidation). Both are immensely popular, both feature famous big-screen and stage actors and filmmakers, both set in the same post-war timeframe (Moscow for the former, and 1946 Odessa (now in Ukraine) — which is considered the time and one of the birthplaces of modern Russian organized crime — for the latter) that allowed (or tempted) for swift retribution against the bandits (much like post-war Italian authorities at times dealt with their Mafia). One of the distinguishing characteristics, however, was, perhaps, the attitude: the heroes of earlier film may have followed the mantra of “the ends justify the means” while the 2007 series emphasised the drive to definitively prove the guilt of suspects.

Italian Octopus in Context of Eeastern Bloc Broadcast

In the 80s one imported TV-show was allowed on Soviet TV and became very popular. It was European (chiefly Italian) production La piovra (The Octopus, ????? in Russian), famous amongst other things for music by Ennio Morricone. I would imagine (no sources yet) that it was put on TV to show the dark side of the glossy appearance of European life. It had very different mood from the shows like Liquidation or The Meeting Place.

While those films still made social and cultural commentary (Liquidation more openly so, obviously, as it did not have to tip toe around Soviet censure), ultimately good guys as the agents of people’s will prevailed against creeping criminal threat (historically as well, as organized crime largely remained underground, in direct opposition to the powers that be) akin the gunslingers of Wild West even if there were less shooting and more detective work.

The Octopus, however, presented grim picture of society so thoroughly and pervasively corrupt by the grip of Mafia’s tentacles that the scene of Michele Placido’s character beating his fist into the bloody pulp against the concrete wall in frustration after losing his loved ones could serve as a perfect metaphor of what obstacles law enforcement had (mayhaps, still have) to deal with. The show that ran from 1984 to 2001 was not only popular, but also influential. Former Italian Prime-minister and media tycoon Silvio Berlusconi, himself under investigation for involvement with the Mafia, in 2009 threatened to strangle writers of The Octopus for giving Italy a bad name.

You might be interested to read the work of Jennifer Ryan Tishler, a professor of Russian at Dartmouth. Below is an excerpt from her article Menty and the Petersburg Myth: TV Cops in Russia’s ‘Crime Capital’ (menty is slang for cops; the show in Russian is called Ulitsy razbitykh fonarei which means Streets of Broken Streetlights). Her article also references a show called Banditskii Peterburg.

Although Streets of Broken Streetlights is a television series about the work of militsionery (police officers) in St. Petersburg, it does more than merely depict Petersburg as Russia’s crime capital. The series explores several avenues of the myth of Petersburg, including its celebrated architecture, its unreal and phantasmagoric quality, and its status as the cradle of Russian literature. Although the television cops seem awash in crime week after week, references to the enduring Petersburg myth send the implicit message that the city, which has endured floods, revolutions, blockades, and benign neglect, will also survive this infiltration by criminals.

The complete article is about 14 pages long, and was published in the Journal of Criminal Justice and Popular Culture.