Contrary to very popular misconception, propagated by fiction books and novels and propaganda non-fiction, it did not. In its basic objectives and functions, Gestapo (not-so-Secret State Police) was a typical political police force. Its primary objective (raison d’être) was to investigate political crimes (crimes against the Nazi state), identify the perpetrators of these crimes and hand them to the prosecutors to be prosecuted and subsequently tried in Nazi courts (e.g. the infamous “People’s Court”).
Contrary to the popular misconception, Nazi legal system did follow rules and procedures required by the “due process”. Consequently, the fundamental objective of any Gestapo investigation was to collect enough evidence (e.g. information) that the individual in question did, indeed, commit the political crime in question.
Sufficient for the prosecution to bring this individual to a Nazi court and for the court to convict him (or her). Unlike the Soviet GPU/NKVD/MGB (which, though also being a political police, had a fundamentally different objective), Gestapo did not consider confession a sufficient reason to convict the individual in question.
Neither did the Nazi prosecution (or the courts for that matter). They needed hard evidence. Which is simply impossible to obtain by torturing the suspect, because the latter will say literally anything to stop the pain. In other words, provide investigators with totally irrelevant, misleading or simply false information which will take lots of man-hours to investigate and confirm.
Consequently, in reality Gestapo relied mostly on good old police investigation and interrogation techniques (it was first and foremost the police). Which is not surprising because initially it was staffed with career policemen known not for their Nazi credentials (in most cases they were not even members of Nazi party), but for their professional competence.
Surprisingly accurate depiction of a typical Gestapo investigation (as well as Nazi prosecution and People’s Court proceedings) is presented in a 2005 German (!) movie “Sophie Scholl – The Final Days” (Sophie Scholl – Die letzten Tage).
It is also worth noting that Gestapo was explicitly prohibited by law to investigate Nazi Party members and the military (soldiers and officers of Wehrmacht). The law was strictly observed and became the key reason why Gestapo failed to uncover the preparations for July 20th coup (or any other coup or assassination attempts).