Police said they received a call before noon from the victim's son, a Los Angeles Police Department officer. They said he discovered his mother's body at her home in the 1600 block of West 66th Street.
Detectives said the officer, who was not identified, was with his mother on Saturday and dropped her off at her house about 7 p.m. He called her Sunday morning, but she didn't answer the phone. He went to her house to check on her and found her in bed with a gunshot wound to the chest.
Detectives said there were no signs of forced entry at the house, but have few other details about the case.
"We don't have any motive, all we know is that she was found dead of a gunshot wound," said LAPD Capt. Dennis Kato. "Other than that, we have no idea what the motive was, whether it was robbery, a burglary, a dispute of some kind."
"That's an 81-year-old woman," said neighbor Irene Devance. "It's a tragedy. So close to home."
The victim's son is a veteran officer who works at the police academy training new recruits.