There is virtually no crime, because this is punished very badly. Often even by death. The King is the judge in all cases, except in the minor ones such as theft, in which the Royal guards can act as judges. Crime isn't really necessairy either because everything that a Saiya-Jin requires is freely available to him.
Murders happen sometimes, but are usually an accident. The Saiya-Jin will get a beating and will be on their way.
The smaller crimes are usually commited by slaves. Pulling at a Saiya-Jin's tail in bad intention will be an immediate death sentence.
Stealing or any other minor crime is usually punished by a beating and no food for the next few days.