Authorities said the shooting happened at about 5:45 p.m. at The Exchange Apartments on Leona Street, just north of downtown.
Within minutes of getting reports of a domestic dispute and assault in progress, police say two officers arrived and knocked at the suspect's door.
"They were knocking on the door and ringing the doorbell and then the suspect just opened the door and began discharging," Asst. Chief Ben Tien said.
Police say the officers, who weren't injured, took cover and returned fire as horrified neighbors watched in disbelief.
"We was coming and the police just kept coming, coming, coming," Denise Johnson said. "I thought they was chasing somebody."
"This is a very prestige neighborhood. Nothing never happens," Renell Strauss said.
Police eventually made their way into the apartment and found an uninjured woman and the dead suspect, who police described as a man in his 20s.
They say he had two guns in his possession, but police weren't sure whether he was firing both of them.
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