I'm a little more suspicious of the woman with the black hair since reading the english version. That she mentions her inability to reach the window before even discovering the body seems meant to dispell suspicion from her since it's a 'locked room case.'The ac is definitely a big part of the case. Maybe it was used to cause the murder, made useless in an attempt at a dying message, or was utilized to keep the body from stiffening for a time trick. However, if the blood is coagulated, I think the last couldn't be used...