Nancy Motes was found in a bathtub on Sunday in what is believed to be a suicide.
The family have issued a statement about the loss, saying: "It is with deep sadness that the family of Nancy Motes ... confirms that she was found dead in Los Angeles on Sunday of an apparent drug overdose. The family is both shocked and devastated."
Nancy, 37, was the daughter of Roberts' mother Betty Lou and stepfather Michael Motes. She was also aunt to American Horror Story actress Emma Roberts. She had been working as a professional dog walker and pet-sitter at the time of her passing.
Julia skipped an Academy Awards luncheon in Beverly Hills - which she was due to attend to promote August: Osage County - to grieve her loss.
Julia and Nancy had a history
Craig R. Harvey, chief coroner of investigations for Los Angeles County, told The New York Daily News: "The decedent was found in a bathtub that contained water. There were prescription and non-prescription drugs found at the scene. The role the drugs may or may not have played is not yet known."
An autopsy is planned and additional toxicology tests have been ordered to find the cause of death.
Speaking of her relationship with her famous half-sister, Nancy said last year: "I think we're both trying to change our opinions of each other. It's a work in progress. It's not going to be fixed overnight."
Nancy had struggled with her weight, and underwent gastric bypass surgery in June 2010, and had said Julia, 46, used to tease her about it.
She explained: "When I was in high school and she was an adult, she would just let me know that I was definitely overweight. It just makes me feel incredibly hurt and very sad."
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