Unlike the modern age of western civilization, how criminals are dealt with in Slothjemia, and for that matter, anywhere in the world in which it is set, will seem completely primitive. While the policing is closer to what we can identify with in the near-modern world, the judiciary is something else entirely.
After a criminal is apprehended, they are formally charged with a crime by an appropriate official from the office of the Lord Prosecutor. The case is then constructed, and presented to judge that works in the office of the Lord High Magistrate. The accused is allowed to give testimony, and both the prosecutor and defense counsel (which will only be present for clients that can afford it themselves, or who have a patron willing to foot the bill) are permitted to call witnesses to bolster their claims for, or against, the state’s case. There are no divisions in the judicial hierarchy for criminal offenses, such as by county, grafdom, or whatnot. But the seriousness of the offense dictates the level of scrutiny it is given, and that can grow substantially during an investigation.
Nobles are entitled to have their cases heard directly by the Lord High Magistrate rather than a lesser official, even if the case wouldn’t ordinarily warrant such a high level of authority. And anyone serving as a Graf is allowed to ask for the Empress herself to hear their case, an extraordinary occasion, to be certain. In no case are their juries, as such a concept is utterly alien to this culture. Nor are there any appeals to a higher authority, except for nobility, and they may, if they choose, appeal to the Empress should they be found guilty. It is rare for her majesty to ever meddle in such things, however. She would prefer her judges to be given their just power, and leave it at that.
Now as to punishment, this is where things get unpleasant. Forced labor is a common punishment for many lesser crimes, but so is simple imprisonment, restitution, or things like a public flogging. In very unusual cases, such as prominent criminals with a strong connection to powerful people, long term incarcerations are possible. More commonly, people that commit grievous crimes are simply executed. To prevent shenanigans in a magical world, where resurrections and the like are possible with the help of sorcery, spellcraft, or enchanted items, executed prisoners are immediately, and with witnesses present to the fact, cremated and their ashes scattered according to the dictates of the presiding judge.
On the issue of torture during the investigative process, let us simply say that the infliction of physical pain to extract a confession is illegal throughout the realm. However, there are other ways to get information from a suspect, or even a witness to a crime, and while some of these ways might be incredibly unpleasant, they are nonetheless admissible in court.