The Collected Cases of Duchess, PI — Laura Anne Gilman

The Alley is no place for the innocent, the unwary, or the just plain
foolish. But if they didn't exist, Duchess would be out of work. For a
fee, she can solve your problem - or make it go away. When trouble's
on your tail, and you can't go to the cops, Duchess is the cat you want
in your corner.

However, not even the best PI can solve every case, and her connections
- from an up-and-coming police dog to a would-be thief-in-training - get
her into trouble as often as they get her out…

Including:

The Case of the Tom in Trouble
Spark to Tinder
The Case of the Feckless Ferrets
Scales of Justice
The Case of the Seaside Swindle