I just finished it.
Chronologically it takes place between case 2 and 3 and is about the first case Phoenix had after getting his badge back.
It doesn't have much to do with the main plot, obviously, since it's an optional case, but it has murder mystery and some character-stuff (we learn Blackquill likes penguins) and humor. Also penguins. Also you get a new optional costume for Phoenix, so now you can dress him in a pink sweater for court.
There's a lot of anime-cutscenes, characters and new places (also penguins) and it took me 7 and half hours to finish, so I'd say it pretty good value for €4.99, (or $5.99, or £3.99).