Looking for depictions of such in fiction. (Non-fiction if you’ve got it.)
“Criminal” in scare quotes for obvious reasons but work with me here, I’m holding half of my babies and can’t type enough to explicate.
There wouldn’t be any crimes in anarchist societies, just as there wouldn’t be any in libertarian ones. See, everyone has agreed to play by the same highly artificial rules, so… no crime.
Snowcrash isn’t exactly anarchist, but close. It talks a little about the criminal justice system (e.g., tattooing “poor impulse control” on the forehead rather than a prison sentence), but not so much about actual crime investigation.
There are several books/ articles written about the customary law system used in Somalia (the “xeer”) and how it works in the (current) absence of a centralized government. Here’s a brief article with references.
David Friedman has written extensively on the medieval Icelandic legal system which lacked an executive branch. This article gives a good introduction as well as links to information about other semi-anarchic legal systems.
Most of the work I’ve seen focuses on the trial and law-making aspects of these systems rather than criminal investigation.
Ursula LeGuin’s The Dispossessed maybe? (It is a long time since I read it.)
Browse around this site and you’ll likely find something:
http://www.bigheadpress.com/index.php
L. Neil Smith (whose Probability Broach is adapted therein) has written some novels on this theme also.