Martin Short was concerned after he hadn't heard from his daughter in over 24 hours, so much so that he called a friend to ask them to check on Katherine ... and then she was found dead.

The Los Angeles County Medical Examiner just released Katherine's autopsy and it reveals how Martin helped police track her down after she went MIA ... only to find her with a self-inflicted gunshot wound to the head.

In the autopsy, obtained by TMZ, investigators say Martin asked a friend to go to Katherine's Los Angeles home, where they found a note on the bedroom door, which was locked.

The friend called 911 and cops made a forced entry into her bedroom ... inside they found Katherine dead in bed with a Glock 19 9mm pistol under her chest.

As we reported ... a suicide note was recovered.

The autopsy says Katherine had a prior suicide attempt in 2017 involving pills ... and she had a documented history of depression and other mental illnesses.

Katherine, the eldest child of Martin Short and Nancy Dolman, was only 42.

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