You need to fight the crimson kimono to find the key,you need to go to the entrence were the door has boards blocking it,after you will see drawers right by the door to the right side of Mio,open it then you will need to fight the crimson kimono,after head towards the normal size tatami room were the closet that you couldnt open is try to open the closet when it says that you cant open it,take a few steps back and the youll have to fight the crimson kimono again(when will she ever learn that i dont have her brother!)
when you beat her she will leave the key behind to open the door for Mayu!
so thats all!