The modern Westernized legal system is by no means the only way that things have been mediated throughout human history. It should be no surprise that parahuman legal systems vary widely as well.
Pallene: The Houses prefer to handle things internally whenever possible. The House Primus is responsible for settling disputes between members of their House and is even empowered to impose penalties for misdemeanor crimes against other members. When disputes arise between people in different Houses their Primii will try to sort something out first. But crimes against another House, or torts that get out of hand, the parties involved hire an Arbitrator from the Civil Guard, paying equally. Arbitrators are also called in for every instance of a felony, and especially in the case of murder. Premeditated murder carries an unambiguous death penalty, voluntary manslaughter (“spontaneous murder”) may be reduced to a hefty fine and probation for up to a century under drone surveillance or house arrest. Conspiracy to commit murder merits exile to an Outworld. Lesser penalties tend towards fines and probationary periods that might be reduced if the convict goes to therapy. Punitive incarceration is unheard of.
Gepatrono-klientoj contracts establish somewhat similar legal relationships between patron and client to that between a Primus and their House, but with a key difference. Nobody can be compelled to testify against another member of their House save in the case of capital offenses, but a patron can be made to testify against their client while the inverse is not true. However, patrons are also required to pay their clients’ legal fees and unofficially expected to use their connections in the oligarchy behind the scenes. Simply having a client who’s been convicted of a crime is a stain on the patron’s reputation, if the patron were to break contract when their client got arrested it would be even worse. In fact many Pallene oligarchs have become known for recruiting clients from members of less-wealthy Houses who’ve been accused of a crime.
Cetan: Old system: A caste-based system, when both parties were of the same caste they were judged by a local elder of their caste. For Labor-majority villages this was typically the village headsman. However if the dispute involved members of different castes a judge of the warrior-noble caste was called in. The warriors themselves benefited from a privilege similar to the kiri-sute gomen of Japan’s medieval samurai, allowing them to pass judgement and sentence on commoners who offended them. It was uncommon but not unknown for a commoner who bumped into a warrior on the streets to be cut down on the spot.
Federated: After contact with Alpha Centauri and the formation of a central government the warrior-nobles’ relative power has steadily eroded. Judges are now certified by a central testing system, with others prohibited from passing judgement regardless of caste. More recently it became possible for judges of any caste to arbitrate inter-caste disputes, so long as the judge doesn’t share a caste with either party.
Eridani: The Eridani Directorate (Inc) relies heavily on their surveillance system to detect crimes and dispatch security officers rapidly. Officers will then subdue (if necessary) and issue fines on the spot. The accused can attempt to appeal, but usually they’ll be lucky if they’re allowed to pay gradually. Very little private property in EDI areas is not owned by the company, with residents only leasing it, and the company tends to rate crimes based on damage to its’ property first and the livelihood of residents and employees second.
I recommend looking into David Friedman’s Legal Systems Very Different From Ours for more information.