Investigators were looking into the possibility that Lance Anderson, 60, shot his sister to relieve her suffering after she spent four years in the care home since coming out of a coma, said Los Angeles Police Detective Juan Santa.
He was suspected of also killing his wife in their shared home before shooting his sister, police said. Anderson was arrested and bail has not been set.
"Mr. Anderson made a unilateral, fateful decision to take two lives and forever alter his and so many others who loved his wife and his sister," Los Angeles Police Lieutenant Paul Vernon said in a statement.
"The motives and rationale for this kind of shooting can never be justified legally," said Vernon, who heads the detective division investigating the killings.
Police said Anderson shot his sister, Lisa Nave, as she lay in her bed at the Country Villa Sheraton Convalescent and Rehabilitation Hospital in the suburban North Hills section of Los Angeles.
He then announced that he was walking to the adjoining patio to wait for police, and ultimately surrendered without resistance, the police statement said. He left a small caliber revolver believed to be the one used to kill his sister on the table next to her, the statement added.
Los Angeles County sheriff's deputies went to the man's home in Santa Clarita, north of Los Angeles, and found Anderson's wife shot to death, the agency said in a statement.
The sister's husband had earlier expressed concern about the wife's fate, Vernon said.
Television station KNBC, an NBC affiliate, reported that neighbors in the area say they heard what sounded like fireworks on Tuesday night but no one called police. Neighbor Grace Madrigal told the station Anderson doted on his wife, who police said had health problems.