Cutie Cop ~Nusumareta File no Nazo~

Cuty Cop is a game modeled after a Japanese TV show quiz, but with a background story: valuable papers have been stolen from the police department, and the only clue is a perfume smell, which most probably indicates a female TV star. The protagonist, a young female cop, has to participate in a quiz and give correct answers to questions related to Japanese TV shows. Each round has four questions, and if the player has chosen more than two wrong answers, it's game over. "Defeating" an opponent in a quiz leads to the next round against the next opponent.

[From Mobygames]