Martin Short’s daughter Katherine was found behind a locked door and with a “note” nearby, TMZ has learned.

Law enforcement sources tell TMZ … Katherine’s friend was the one who called police after she hadn’t “been heard from in 24 hours.”

As we previously reported … Katherine died from a self-inflicted gunshot wound Monday at her Los Angeles home. Sources tell us a “note” was found nearby … along with a gun.

We’re told homicide detectives also responded and ruled out foul play, sources said.