The assailant then entered the busy shopping mall and wounded at least two other people.
However police officers investigating the seemingly random attack are looking into the possibility that the gunman, who was later shot dead by officers, was linked to an earlier murder in the area.
Police were called to the home of a murdered 67-year-old woman at 14:00 local time (19:00 BST) and found the car of the deceased woman missing.
After the police put out a description of the car to other forces in the area, the gunman was found to be driving the vehicle. Yet when a police officer pulled the assailant over, the gunman shot the policeman in the arm and fled. The officer was taken to hospital but his injuries were not said to be life-threatening.
However, 15 minutes later police received reports of the shopping centre shootings.
"It was just mass chaos, as you can imagine, on a Sunday in a crowded mall," Sergeant Tony Sanders told reporters.
The shooting comes just under two weeks since the Virginia Tech university attack which saw 33 people, including the gunman, shot dead. Since the shooting, said to be the worst mass shooting in the US, tensions in the country have continued to rise as fears of copycat attacks remain.
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