The best source I've encountered on regular law enforcement in the USSR is Policing Soviet Society: The Evolution of State Control by Louise Shelley. She provides a very interesting critical overview of the evolution and functions of Soviet law enforcement — I highly recommend that you find a copy of the book if you're interested in reading more.

The civil police, the militsiya, were a significant part of the USSR's repressive security apparatus. From 1925, the militsiya fell under the administrative control of the People's Commissariat for Internal Affairs (NKVD), which became the Ministry of Internal Affairs (MVD) in 1946. (Other departments of the NKVD included GULAG, which administered the USSR's prison and labour camps, and the OGPU/GUGB, the intelligence and secret police service which eventually evolved into the KGB.)

During the Stalin era, brute-force repression was the state's primary tool for crime suppression. Known criminals were subject to harsh sanction, including prolonged confinement in the gulags. Those considered potential risks to security and public order were systematically isolated and removed from the USSR's major urban centres.

Criminal justice, like almost everything in the USSR, was centrally-managed and highly bureaucratised. It was also highly politicised, both directly and indirectly. The miltisiya had a political mandate to support and strengthen the Soviet state, and in this ideological role were a visible counterpart to the chekists of the GUGB/KGB. But law enforcement and the judiciary were also on the receiving end of constant, more pedestrian Party pressure to cut ordinary crime rates and demonstrate results.

The Soviet Union generally showed materially lower crime rates than the Western countries — but those numbers were often artificial, and primarily achieved through aggressive policing, the judiciary's prioritisation of 'clearance' over justice, and near-constant manipulation of statistics at all levels.

The militsiya was commonly under-funded, under-resourced and under severe political pressure. That's not a recipe for effective policing: the USSR manifested endemic problems with under-reporting of crime (from downgrading crimes to less serious offences to totally failing to record that crimes even occurred), highly deficient investigative practices and the willing compliance of a judicial system that was designed to produce, convict and punish a culprit as quickly as possible. As Shelley puts it, "the Soviet legal system operated on the assumption that it was better to convict ten innocent men than let one guilty man go free."

In the early post-civil war years, and under Stalin, the militsiya had overwhelmingly been staffed by working-class men, with limited education. Under Khrushchev and Brezhnev, the MVD took steps towards professionalisation and introduced more rigorous training and educational requirements. But militsioners' salaries consistently lagged behind those of many skilled labourers and professionals — which naturally led to endemic corruption.

Ultimately, the Soviet civil police were broadly ineffective as a law enforcement body — as evidenced in part by the spiralling out of control of crime rates and the rise of organised crime in the 1980s — but they were an important part of the Soviet organs of security and control. There are complex social and economic reasons underpinning the ebb and flow of crime in the USSR, but ineffective, corrupt and ideologically-rigid policing seldom helped the situation.

Most of the work that has been done is on the NKVD, KGB, etc. And that's the work I'm more familiar with. I assume you are asking about day to day "regular" police officers, people who worked as members of the militsiia rather than about those organizations. The best I can do is try to point you towards something I've just searched up.

My feeling is that the kind of thing you are interested in would likely be of more interest to political scientists/ "policy" people. A quick search around shows a couple of articles that I have not read, this one looks closest to what you are interested in:

The soviet Militsiia: Agents of political and social control. Policing and Society An International Journal of Research and Policy Volume 1, Issue 1, 1990

Here is the abstract:

The paper provides an overview of the development of the Soviet militsiia (regular police) and its present structure, organization and functions. The paper concludes that the nature of Soviet policing differs from that of western democratic societies. Policing is a state monopoly; the militsiia closely controlled by the party with minimal input from the citizenry. Its responsibilities are broader and it is more intrusive into the daily life of the population.

Since the revolution, the militsiia has had three primary functional areas—social, economic and political control. The functions of the militsiia have changed with the development of the Soviet state. The political responsibilities have receded but remain more important than in democratic societies.