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An officer opened fire, killing Smith, a 31-year-old resident of Compton.
One officer was apparently also hit in the leg, but is expected to be OK.
"When he slipped, he just kept slipping, and they just kept shooting him," said Kalonna Lacount, Smith's fiancée.
While police said Smith was armed, witnesses said there was no gun.
"If an officer got shot, it had to be by one of their own," said witness Clifford Roach.
Lacount and activist Morris Griffin also said Smith did not have a gun.
"His back was turned. They killed my brother," said Smith's sister.
There are two separate investigations into the shooting, one by the police department, and another by the District Attorney's Office.
The Inglewood Police Department is facing scrutiny by the Department of Justice after several shootings in the last two years left four people dead. Kevin Wicks, a 38-year-old postal worker, was shot and killed in July 2008, and a homeless man was shot to death after police said he reached for a toy gun stashed in his waistband.
Anyone with information is urged to call the Inglewood Police Department at (310) 412-5246.