An unarmed man who was fatally shot in Bakersfield, Calif., by an officer who thought he had a gun was actually carrying a crucifix, the police say.

The family of the man, Francisco Serna, 73, who said he had dementia, is demanding a Justice Department investigation into the actions of the Police Department, which previously came under scrutiny for its use of deadly force.

The Bakersfield police chief, Lyle Martin, said at a news conference on Tuesday that officers did not find a gun on Mr. Serna after he was killed on Monday and that the department was conducting its own investigation into the shooting.

According to the police, a woman who lives across the street from Mr. Serna was removing items from a vehicle outside her home when she noticed a man standing behind her. He turned out to be Mr. Serna. She said he asked if he could get in the car. He was allowed only to look into the vehicle, and the woman went inside her house, the chief said.