The man told the workers "he killed people" and allegedly tried to stab one of the employees. The man then ran to the back room and locked himself in a walk-in refrigerator.
Responding officers said when they got to the market there was a trail of blood from the front of the store leading to the refrigerator.
Investigators said the man jumped out of the refrigerator holding an ax. The suspect then allegedly raised the ax over his head and lunged toward the officers.
They responded and opened fire, killing the man.
Investigators are looking into the possibility that the man was mentally ill.
The two officers who fired their weapons were identified as Sgt. John Knapp, a 28-year veteran, and Sgt. Greg Held, a 9-year veteran. Both officers have been put on administrative leave.
"They could have used their Taser guns. Why do they have Tasers? Why do they have training?" said Inglewood resident Jose Alejo.
Other Inglewood residents echo Alejo's concerns and are wondering if the officers needed to use deadly force to subdue the suspect.
"They could have had another way of handling it other than shoot the man dead," said another Inglewood resident Yolanda Roth.
There have been several officer involved shootings in Inglewood in recent years.
"To me, it's really not that unusual for something like this to occur. Obviously, Inglewood police is known for using brute force in a lot of cases," said Inglewood resident Giana Zelaya.
The name of the suspect has not been released.
The Inglewood Police Department is conducting separate criminal and administrative investigations of the shooting. The Los Angeles County District Attorney's Office is also conducting an independent investigation.