Restorative Justice, which a post-scarcity communist society would definitely have, dictates that the compensation for crimes should be focused around making the aggrieved whole and ensuring the aggressor no longer does the egregious action. In a murder case, that could amount to requiring you to do service for the deceaseds family for years, since you can never fully make them whole. Punishment does not work, and would not be a primary motivator in any Star Trek universe, because it doesn’t resolve any of the problems and only creates more.

So in all likelihood, civil cases would be solved through reconciliation, restoration, and education to prevent further such issues.