Jacob D. Robida, 18, was shot twice in the head and "it doesn't look good right now," said Massachusetts prosecutor Paul Walsh Jr.
Walsh said the teen shot Officer Jim Sell, 56, twice during a traffic stop in this northern Arkansas town.
About 25 miles away, Robida sped over spike strips set out by state troopers, but continued to drive with two punctured tires into downtown Norfork. Robida's car then careened into several parked vehicles to avoid a police barricade.
"When he wrecked he started firing at our officer and a state police officer and the officers returned fire," said Baxter County Sheriff John Montgomery.
Walsh said the teen shot his unidentified female passenger before he was wounded in the shootout with police.
Robida was taken to a Springfield, Mo., hospital, according to state police spokesman Bill Sadler.
Investigators had searched for Robida since Thursday's attack at a bar in New Bedford, Mass., that left three men wounded, one critically.
The hatchet used in the attack was found outside the bar, but detectives believed Robida still had the gun.
Robida was a high school dropout who friends say glorified Naziism but never expressed any specific prejudice against gays.
"This is insane," said Heather Volton, 22, of Fall River, Mass., who had known Robida for more than a year. "That kid never so much as raised his voice at me ... This is all pretty much a shock to me, like everyone else."
Scott W. Lang, the mayor of New Bedford, speaking at a news conference Saturday evening, said that his community's hearts are with those in Arkansas. He said that they have "a tremendous debt and sympathy for everything."