As it is in any world filled with people, there is crime in the Sea of Stars, from petty to the most serious. Many places do not have organized group dedicated to solving crimes, keeping the peace and enforcing law, yes, actual investigation and crime solving as we have come to expect in the modern world, only very rarely.
Those who investigate crimes are usually known as Inquisitives or more rarely Investigators or Detectives (and occasionally other names as well), depending on the place they may be operatives of the powers that be, direct agents of the ruler, or even freelance professional, solving crimes for a fee (consulting inquisitives, you might say). While these people are seek to solve crimes, they do so in various ways and with varying levels of support from the authorities.