Sotomura Tanteisha no Manekarezaru Kyaku

Matsuda is a private eye who runs his own detective firm, taking on quirky cases centered around the local shopping arcade. He's recently taken on a new roommate (and lover) named Kamiko who is unemployed, ruthlessly horny, and was actually a classmate of his from his past. While the two work together to solve cases, they carry on in what starts as a strictly physical relationship, but which by and by evolves into one that neither wants to lose.