Minai Madoka is the younger sister of the young and diligent and elite detective at Kakiuchi Police Station, Minai Tomoe and the daughter of the Metropolitan Police Department's successful and famous detective, Minai Yūsuke. Despite looking similar to Tomoe, Madoka's personality is the exact opposite of her sister's. Madoka is cheerful, carefree and easily expresses herself, but she acts rather childish sometimes and likes to slack off at work.
According to Tomoe, Madoka's personality drastically changed after the tragedy at the Minai household in 1971. Madoka and Tomoe lived in a happy family, but all of this was destroyed, when their house completely burned down. The two sisters survived, but their parents burned to death in a fire. Tomoe and Madoka witnessed their parents' charred corpses, which traumatized Madoka who was only at junior high school then. It took a year for Madoka's psyche to recover, but even after the recovery, she developed pyrophobia, her grades dropped, she started to skip school and hang out with a bad crowd. Due to her change of personality, Madoka's relationship with Tomoe became cold form the constant arguments, until the two sisters treated each other as strangers. Her relationship became better with Tomoe after they've started working at the same police station, but the two sisters still end up in serious fights over minor things, as it was seen in Kagebōshi-hen. Even though her bond with Tomoe is really strong, there's an underlying tension between them, due to Madoka's marriage to Yamaoki Kaoru, another police officer who is more than 30 years older than her.
Unlike her father and her sister, Madoka is not enthusiastic about being a police officer at all. It was mentioned in Kagebōshi-hen that she was just invited to take the recruitment exam and she ended up with a job.