3 ideas
A sealed door, a stamped wax seal or a watched threshold does not prove that nobody entered. It proves only that nobody entered in the way the observers expected. The locked-room puzzle works because witnesses treat the seal as the event, when the real action happened before the seal was set, after it was broken, or through a route nobody was watching.
When an event looks supernatural, treat it as an escape artist or illusionist would. Ask what the audience was made to watch, when, and from where, and look for a double, a switch or misdirected timing. Apparent bilocation or a vanished killer usually comes down to controlling where witnesses look and what they assume is continuous.
A community that already believes a room is haunted will accept a ghost as the explanation and stop looking for a human agent. A killer who builds on that belief, through legend, séance and uncanny signs, gets investigators to rule out the ordinary. The mystery is solved only when the detective declines the supernatural frame and asks who gained from everyone believing it.