Himitsu no Hanazono

A high-school student named Kōsuke had a dream, in which he saw a beautiful woman talking to him. The next morning he found out that the new teacher looked very similar to the woman he saw. After overhearing a conversation, Kōsuke realizes that the new teacher is in fact a detective sent to investigate the murder of a female student that occurred in the gym. The young man has to play his cards right in order to become part of the investigation, solve the mystery, and perhaps impress the attractive teacher in other ways.

[From MobyGames]