Police said he had a wound to his arm.
"She didn't want the girl over there anymore", Egland said.
She is believed to have been injured and forced into the vehicle after the gunman shot his grandmother.
During the chase, Atkins fired at officers, blowing out the car's back window, and there was more shooting before the auto crashed into a pole outside the Trader Joe's, followed by another shootout with police, Police Chief Michel Moore said.
Melyda Corado is seen in a GoFundMe
Police aren't sure what led to the initial violence that produced the vehicle chase and standoff.
More gunfire ensued before Atkins crashed into a pole outside the supermarket.
It's unclear whether Atkins or an officer shot Corado, Moore told local media outlets, though he confirmed she suffered the fatal injury while escaping the store along with other trapped employees and shoppers. Officers escorted the girlfriend from the vehicle.
Police believe a man involved in a standoff with officers at a Los Angeles supermarket shot his grandmother and girlfriend before firing at officers during a pursuit, then crashing outside the supermarket and running inside the store. It wasn't clear if employees or customers were still inside the store.
"I was working in the backroom, heard screaming and gunfire, ran upstairs, grabbed a couple co-workers, made my way to into a back section of the storage area upstairs", Gerace told CBS2.
The standoff inside the Silver Lake Trader Joe's dragged on for approximately three-and-a-half hours until Atkins finally surrendered without further incident at about 6:30 p.m. He was identified as 28-year-old Gene Evin Atkins, who was booked on suspicion of murder.
The scene inside the store was described as "chaos" with one woman reporting to a local television news outlet she was almost trampled trying to escape.
Fire officials said six people, ranging in age from 12 to 81, were taken to the hospital.
Authorities say the man shot his grandmother and girlfriend earlier in the day.
Officers with the Los Angeles Police Department were pursuing the gunman, who is suspected of shooting an "elderly woman" and "a woman in her 20s" in the area of South Central around 1 p.m., LAPD Officer Mike Lopez told HuffPost.
The Los Angeles Police Department (LAPD) in the United States said on Saturday that they had arrested a suspect after a tense standoff in a Trader Joe's grocery store in the Silver Lake area. Trader Joe's also released a statement on the fatal hostage situation: "Our hearts are broken over what happened today". A makeshift memorial of flowers, candles and notes grew on the sidewalk outside of the store on Sunday. His grandmother had tried to help him find employment and "was just trying to make him do better", she said.
The man began shooting and ran into the Trader Joe's store where he barricaded himself inside. When police returned fire, Field and others got down on the ground, he said. "Our thoughts are with her family, and our Crew Members and customers who experienced this terrifying and unimaginable ordeal".
The suspect barricaded himself inside the supermarket with an unknown number of people, but was taken into custody "without incident", according to police.