Martin Short's Daughter Katherine Had a Service Dog for Her Mental Health

Katherine Short had a dog to assist with "mental illness" over the years ... this according to her now-deleted professional website.

The daughter of Martin Short -- who passed away Monday -- had a biography tab dedicated to her pup, according to Page Six ... who reviewed the website before it was taken down.

Katherine says the dog -- named Joni after singer-songwriter Joni Mitchell -- was her "incredible service dog, who has been assisting me with my own struggles with mental illness for the past 5 years." It's unclear when the bio was written.

Short also wrote Joni is a sweetheart who loves people ... so clients visiting her office shouldn't be surprised to be greeted by the happy dog with a tail wag and a kiss.

We broke the story ... the Los Angeles Police Department and LAFD firefighters responded to 42-year-old Katherine's Hollywood Hills home around 6:40 PM PT Monday where they found her at the scene, already deceased.

Law enforcement sources told us she died from a self-inflicted gunshot wound. A representative for the Short family told TMZ ... "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 -- the eldest child of Martin Short and Nancy Dolman -- worked as a social worker in Los Angeles.

Martin Short had comedy shows with Steve Martin in the Midwest scheduled for this weekend. Those shows have been postponed.