MONSTERS

While MONSTERS is mainly focused on Comedy as opposed to the seriousness of the crimes themselves, both that and Kagi no Kakatta Heya are played out very similarly, have slightly aloof, out of the box characters as the main crime-solver and they're both focused on episodes that are sort of fixed (more so Kagi than MONSTERS) and can be watched whenever; watching them in order isn't really needed.

Both are hilarious detective comedies but the formulaic straight man and funny man roles being the experienced detective and the rookie detective respectively. If you're not into Japanese humor then this might not be for you.

regardless of the story, the actors found themselves in characters that fit them perfectly; and are good
(Kamiki Ryunosuke, Katori Shingo, Yamapi / the - incidentally all somewhat anti-heroic - Shizukui Kei, Hiratsuka Heihachi, Saionji Kosuke)
and it's pretty much what holds the shows...