Kaoru is the chief inspector of Kakiuchi Police Station, and the boss of Minai Tomoe, and Fujita Shingo work for. He's also the fiancé of Tomoe's sister, Minai Madoka, who is a fellow police officer at the traffic department of the same police station. Since there is a 30-year age gap between him and Madoka, their marriage is delayed due to Tomoe's opposition. Despite all this, he's on good terms with his subordinates, including Tomoe, and it is shown that his feelings toward Madoka are genuine. In Kagebōshi-hen, Tomoe accepts their marriage shortly before her death, and at the end of the arc, Kaoru and Madoka finally marry and the two of them has a child. The child' name is not known, but Madoka said that if they have a girl, she'll name her after her deceased sister, therefore it's more than likely that their child is named Yamaoki Tomoe. After his retirement, Madoka and Kaoru move to a small village in the countryside.
While his history with Ōishi Kuraudo is unknown, it is shown that the two of them share a similar mentality and they are old friends. Just like Ōishi, Kaoru was also friends with Tomoe's and Madoka's father, Minai Yūsuke, therefore it's possible that the three of them worked together in previous investigations.
As of 1983, both of his parents are alive and they live in the countryside. Due to unknown reasons, Kaoru's relationship is not exactly good with them and they rarely talk, but otherwise they tend to meet up now and then.