A cousin of Mr Atkins, Charlene Egland, told the AP that he had been arguing with his grandmother, Mary Elizabeth Madison, for weeks over Mr Atkins’ girlfriend, who had been staying with them in their South Los Angeles home.
Ms Egland said that Ms Madison “didn’t want the girl over there anymore”.
Ms Madison, 76, had raised Mr Atkins since he was seven years old, Ms Egland told the AP.
Ms Madison was shot after she made a comment about how many television sets Mr Atkins had on, according to Ms Egland. Mr Atkins’ girlfriend was allegedly injured by a bullet as well.
The grandmother, shot a number of times, was in a critical condition, police said.
Ms Egland told the AP she tried to call police after hearing another family member shout: “I think Gene shot my mama!”
Mr Atkins fled his grandmother’s house in her vehicle along with his girlfriend, according to the police.
Police said he fired multiple rounds at officers during the ensuing vehicle pursuit before eventually running into the Trader Joe’s supermarket and holding more than 40 employees and customers hostage for hours.
The woman who was killed has been identified by family members as 27-year-old Melyda Corado.
Her brother, Albert Corado, had asked for information about his sister on Twitter during the incident, and later confirmed she had died.
How did the hostage situation unfold?
During the three-hour siege, people were seen fleeing the Trader Joe’s supermarket, some jumping from windows. One woman was killed.
The suspect, Mr Atkins, allegedly crashed the car and ran inside the shop.
Eyewitness Don Kohles said he saw the car the suspect was driving crash into what was a fire hydrant or a utility pole.
“Then this guy comes out of the car and starts running toward TJs,” Mr Kohles told CNN.
“I look behind me and there were two police guys coming with heavy guns, then boom boom boom boom, so I go into TJ’s and I see this guy and he comes in.
“And I see the two front glass doors shot out. I look around and I see a TJ’s employee laying on the ground.
“We all laid there for about a half-an-hour until LAPD came and got us out. They helped carry me across the parking lot and they sort of tossed me over a wall,” Mr Kohles added.
The Los Angeles Police Department said Mr Atkins asked for handcuffs to handcuff himself before he eventually surrendered.
Six people were taken to local hospitals, officials say, but none had any life-threatening injuries.
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