Police Sgt. Robert Watt says an elderly man is believed to have fatally shot two women before turning the gun on himself in the lobby of the Golden West Tower apartments.
The shooting occurred shortly after noon Tuesday.
Watt says the victims haven't been identified and the motive is unknown. One of the women is believed to have been an employee.
Witnesses are being interviewed, and police are trying to obtain surveillance footage.
According to the city of Torrance's website, Golden West Towers is a 180-unit, privately owned and operated facility. The low- and moderate-income housing is for seniors who can live independently.