Otomo Katsuhiro has the best taste for drawing an Eroica parody manga.
Thanks to @skyblep mentioning that this manga exists, I finally got around to reading this one shot. Cats Head Home at Dawn (猫はよく朝方に帰ってくる - Neko wa Yoku Asagata ni Kaette Kuru) was first published in Young Comic in 1981, and was later compiled in Otomo's SOS Dai Tokyo Tankentai (SOS大東京探検隊) anthology. In the afterword, he clearly states that this hard-boiled detective story was drawn as an Eroica parody.
All Eroica fans should check this manga out to laugh at Detective notKlaus looking for a cat.
Otomo is a Klaus bully.
Bonus: What Aoike said about this manga in her Manben episode (naokiurasawa.com looks down at the moment, but we all know how great of a person the owner of the site is for subbing Manben episodes)