Mayu finds the key on top of the teachers podium inside the classroom 1-A. It's usage depends if you picked up the notebook and the student ID.
If Mayu picked the items above, Yoshiki will read the notes inside the student ID and use the key to unlock the music box and get another key.
If Mayu did not collect the items (locking herself in the wrong end route), she will try to use the key to unlock the reference room, failing. Yoshiki will scrape off the rust off the key and Nana will identify the key as the Lab Key.