(CNN) -- A gunman already suspected of wounding a police officer shot and killed two people and wounded at least two others at a shopping center in Kansas City, Missouri, before being gunned down by police, authorities said Sunday.
"It appears that he came to the mall to shoot people," said Sgt. Tony Sanders, a Kansas City police spokesman. "Whether it was random or not we do not know."
Police are also investigating any connection the man may have had to the death of an elderly woman whose body was found in her home a few miles away, police said. (Watch a witness describe hearing shots and seeing people flee the mall )
Sanders said the man shot and killed two people in the parking lot of Ward Parkway Center, about nine miles south of downtown, about 3:30 p.m.
He continued into the mall, where witnesses said he fired several more shots with what appeared to be a sawed-off shotgun, but police later determined to be a rifle.
Shots near Starbucks
"I was in my truck and the gunman was two cars over from me," shopper Queea Miller told CNN.
She said she saw the gunman shoot in the direction of a Starbucks coffee shop.
"Then, after he stopped, he re-loaded and started shooting again," said Miller.
Miller said during the shootings, she and her 18-year-old daughter leaned their seats all the way back.
"I got to praying. You could hear the shots going off again," said Miller.
Then police, their guns drawn, began "coming from everywhere," she said.
Clothing store manager Lissa Young said "several rounds of gunfire" were followed by two customers who ran into the store and said shots had been fired.
She said she immediately locked the doors and ordered the customers to the back of the store, where they waited until police gave them the all-clear.
Sanders said police shot the gunman outside a Target department store. Investigators have no clue as to his motive, Sanders said.
Officer shot; then mall chaos
The mall shooting took place less than 20 minutes after a Kansas City police officer was shot and wounded on a nearby road -- and about an hour and a half after police found the body of a woman in her home about five miles from the mall.
Officers found the woman dead and her car missing at 1:49 p.m., Police Capt. Rich Lockhart said in a statement issued Sunday evening. A police officer spotted the car on a nearby road at 3:11 p.m. When the officer pulled the car over, the driver opened fire, hitting the officer in one arm.
The 44-year-old officer, a 15-year veteran, was treated and released Sunday afternoon, Lockhart said.
"He had his wherewithal enough to put out a suspect description and direction of travel and vehicle," Sanders said.
"It is believed the dead man [the mall shooter] is the one who shot the officer on Bannister road. His vehicle was found in the parking lot," Lockhart said.
Barely 15 minutes after the officer was wounded, police received the first reports of the shooting at the shopping mall.
In addition to the wounded police officer, Sanders said at least two people turned up at nearby hospitals after being shot at the mall. Investigators were combing through the mall Sunday evening to ensure the gunman had no accomplices, and Sanders called the building "a giant crime scene."
"We have hundreds of witnesses who were inside the mall when he came in," he said.
"It was a Sunday afternoon at a mall in Middle America, so you can imagine it was crowded."