The body of Nancy Motes, the younger sister of Julia and her actor brother Eric Roberts, was found on Sunday. She had been dog-sitting for a friend.
Police said a post-mortem examination had not been performed and there were no preliminary findings about how she died.
The family released a statement that said Ms Motes, 37, died of an "apparent drug overdose", according to People magazine, but noted that no official cause of death had been determined. The statement describes the Roberts family as "shocked and devastated".
Julia Roberts is nominated for an Academy Award for her role in August: Osage County.