Katherine Short 911 Dispatch Audio Released

Dispatch audio recorded the moment authorities raced to a reported shooting at the home of Martin Short's daughter, Katherine ... revealing the person who called in the incident was unable to enter the bedroom.

In the audio obtained by TMZ ... LAFD firefighters are heard responding to a call on Katherine's street Monday evening, initially for a shooting. Later, one firefighter asks if they are clear to enter, then confirms the incident was "self-inflicted" -- stating the caller is there with the patient but unable to enter the bedroom.

TMZ was first to report the devastating loss of Katherine Short, who took her own life Monday at her Los Angeles home. Law enforcement sources told us LAPD and the fire department responded to her place in the Hollywood Hills shortly after 6:40 PM PT, where she was found deceased.

A representative for the family told TMZ in a a statement ... "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 involved with a nonprofit organization called Bring Change To Mind, which works to break down stigmas connected to mental health issues.