Was it any different than in western countries ? Were there any way the socialist ideology was influencing the way those investigations were done ?
For a time-frame, I was thinking of the time between the 70's towards the end of the soviet union.
The Soviet law enforcement system is generally very different from Western policing models, but there are overlaps and analogues. The key difference is that it was law enforcement institutions were markedly more centralised than in most western countries, which tend to administer law enforcement at the municipal or regional levels.
Structurally, responsibility for law enforcement was divided between two organisations:
The latter was at a very fundamental level an ideological organisation: the KGB's foremost responsibility was to serve as the defender of the revolution, and it played a major role in suppressing internal dissidents and enforcing Soviet orthodoxy.
The militsiya, though ostensibly a civil law enforcement agency, were not without a political role. They were, just like the KGB, one of the state's organs of control — and were active participants in the system of coercion and persecution against anyone regarded as ideologically unsound.
But the real ideological pressure on the Soviet police was not that they were forced into any particularly 'socialist' mode of investigation, but that the state's obsession with control and order forced the police to adapt — at the cost of what we would regard as effective investigative or judicial practice.
The generally underfunded and poorly-equipped militsiya had a long heritage of corruption and incompetence, attributable in no small part to the USSR's statistics-obsessed bureaucratic culture. The Party mandated that more than 90% of criminal cases must be cleared, and the police and judicial systems were wholly structured and operated in pursuit of this aim.
Perhaps predictably, in a state where there are few civil liberties, due process and the rule of law (as we understand them in the west) were not major priorities: violent coercive methods against suspected criminals were common, and there was little to no hope of what you'd call a 'fair' trial. The police's main objective was to make an arrest — once they did that, a conviction was likely to follow whether the detainee was guilty or not.
In the west, law enforcement and the prevention of crime are important parts of the civil discourse; police work is scrutinised by the press and the public, and the fair and competent administration of justice is ostensibly a prized ideal. The key difference in the USSR was that the militsiya were in no way (structurally or philosophically) accountable to the public — their responsibility was to state and Party. Their primary objective was the maintenance of order and control, not the defence of some liberal ideal of 'justice'.
I'd recommend finding a copy of Policing Soviet Society: The Evolution of State Control (1996) by Louise I. Shelley if you're interested in reading more. I've consulted it several times in the past, and it's the best text I can think of for an analysis of the structure of the militsiya and the nature of Soviet internal policing (on both the criminal and political levels.) A couple of key extracts for you —
On the USSR's low crime rates:
Low crime rates in the Soviet Union were not the result of a superior police. Rather, the Soviet militia was a central component of an entire system of social, political and economic controls that reduced the possibilities for crime commission in the USSR. The militia enforced measures that restricted individual mobility, removed recidivists from major urban centers and kept released offenders under surveillance. Rather than find panaceas for crime, the authoritarian Soviet state simply created a unique geography of crime in the country, together with a massive imprisoned population which, in actual numbers and on a per capita basis, exceeded that of other industrialized societies.
On the militsiya's investigative process:
The investigative process in the Soviet Union was quite different from that known in the United States and represented a middle ground between an inquisitorial and adversarial system. The particular Soviet twist was to make the examining magistrate a part of the prosecution. Criminal investigations conducted by the principal law enforcement agencies in the USSR—the militia, the procuracy and the KGB—served three basic functions: to detect crime that threatened the social, political and economic order; to locate suspects for reported offenses; and to prepare ironclad cases that could not be discredited by defense attorneys in court. [...]
For many years, the Soviet legal system operated on the assumption that it was better to convict ten innocent men than let one guilty man go free. According to this philosophy, the purpose of investigations was not to solicit truth, but to obtain convictions. The militia was under constant pressure to initiate cases; once a case was opened, Party pressure made it almost impossible to drop, even in the face of insufficient evidence or the arrest of the wrong suspect. A case that did not result in conviction and was sent back for reinvestigation by a judge was considered a tragedy for an investigator. Both investigative and judicial personnel feared case dismissal to such a degree that they went to great lengths to avoid such a disposition, including use of fabricated accusations, false testimony and falsified evidence. Conviction was nearly assured in the cases that proceeded to trial because judges feared reprisals from the Party apparatus.