An autopsy was performed on Katherine Short -- the daughter of Hollywood legend Martin Short -- Tuesday by the Los Angeles Medical Examiner's Office ... and now her body is ready to be released.

As we first reported, Katherine died by suicide Monday inside her Hollywood Hills home -- from a gunshot wound to the head, according to the Los Angeles County Medical Examiner's website.

TMZ obtained dispatch audio, revealing that the person who called 911 from Katherine's house was unable to gain access to her bedroom. Los Angeles Fire Department personnel are heard responding to the scene for a shooting Monday evening ... the incident is later clarified as "self-inflicted."

Martin Short and his family issued a statement, saying ... "It is with profound grief that we confirm the passing of Katherine Hartley Short. The Short family is devastated by this loss, and asks for privacy at this time. Katherine was beloved by all and will be remembered for the light and joy she brought into the world."

Katherine was 42.

RIP

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