Irontown Blues by John Varley

When humanity has been evicted from Earth for the good of the rest of the inhabitants, the remaining colonists on the eight worlds can cope by being Heinleiners, or by role-playing a seedy noir detective and solving mysteries. Chris Bach and his uplifted dog, Sherlock take a case from a woman who was deliberately infected with a disfiguring disease. 

The case leads them through the warrens of the moon, to Chris's mother's dinosaur farm, and into more and more ruthless opposition. 

This is book four of the Eight Worlds series, and while there's some background about the Big Glitch (when the central lunar computer went crazy) that is helpful, there's enough narrative here to establishing the story for new readers. If you're hooked, the earlier books are even better.