Katherine Short died from a self-inflicted gunshot wound to the head … according to her L.A. County Dept. of Public Health death certificate.

We broke the story … LAPD officers and LAFD firefighters responded to Katherine’s Hollywood Hills home last week where they found her dead. Sources told us at the time Short took her own life.

According to her death certificate, she’s been cremated.

Katherine — the eldest child of Martin Short and Nancy Dolman — was found behind a locked door in the home … and a note was found on the scene. The contents of the note are still unknown to the public.

We spoke to a close friend of Katherine who told us her behavior leading up to her death was normal … and, she didn’t exhibit any signs she may hurt herself in anyway.

That said, Short — who legally changed her name to Katherine Hartley in 2013 so social work clients wouldn’t harass her — previously opened up about her mental health struggles.

Martin has reportedly been inconsolable in the days since his daughter’s sudden death … and, he’s retreated from the public eye — canceling multiple comedy shows with Steve Martin last weekend and skipping the Actors Awards at which he was nominated for Outstanding Male Actor in a Comedy Series.

Katherine was 42.

RIP