Jacob D. Robida, 18, died at Cox-South Hospital in Springfield, Mo., hospital spokesman Randy Berger said.
Investigators said the high school dropout from New Bedford, Mass., had dabbled in Nazism, and police there said the attack that injured three men, one critically, at the Puzzles Lounge on Thursday was a hate crime.
New Bedford police said Sunday they were still trying to determine what motivated Robida and if he had any help.
"By no means is the investigation is over," said New Bedford police Capt. Richard Spirlet.
"I wish he would have lived and gone on trial," said Dan Sheterom, 51, who lives above Puzzles Lounge and frequents the tavern.
After the New Bedford attack, police say, Robida picked up 33-year-old Jennifer Rena Bailey at her home in Charleston, W.Va.
"Apparently she's had a prior relationship with this guy and had been corresponding with him. Other than that, we're still in the dark about that," West Virginia State Police Sgt. C.J. Ellyson said Sunday.
"The extent of their relationship I don't know," he said, adding that investigators also didn't yet know how they met.
Bailey was the mother of three children, the youngest of whom was 4. Ellyson said the children were with relatives. He said Bailey was either divorced or separated from her husband.
"What we don't know is if she went willingly or was abducted," Ellyson said.
Spirlet said New Bedford investigators had been in contact with West Virginia authorities even before Saturday's killings and gunfight in Arkansas, but he wouldn't give details. "That's part of the investigation," Spirlet said.
On Saturday, as Robida and Bailey drove through the northern Arkansas town of Gassville, Officer Jim Sell pulled them over in front of the Brass Door Motel and Restaurant for a traffic violation, investigators said. Robida killed the 56-year-old officer, State Police spokesman Bill Sadler said.
Motel manager Maryann Hoyne said she heard three shots, saw Sell on the ground and watched as Robida drove away, then circled the motel.
"What he was doing was retrieving his gun. He had dropped it at the side of the officer," Hoyne said. "He jumped out of the car, picked up the gun, got back in his car and sped off."
In downtown Norfork, 20 miles away, police set up a roadblock as Robida approached.
Spike strips set out by state troopers blew out two tires but Robida kept going, driving on the bare metal rims into Norfork, authorities said. The fugitive's car slammed into several parked vehicles to avoid the police barricade and spun 180 degrees to a stop.
"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.
CBS News correspondent Kelly Cobiella reports Robida shot his friend once in the head and then fired on police. Police fired back, hitting him twice.
Arkansas authorities would perform autopsies on all three of the dead, said David Brown of the Greene County Medical Examiner's office in Springfield, Mo.
Police in New Bedford had sought Robida on charges of attempted murder, assault and civil rights charges. Had Robida survived the Arkansas shootout, he could have faced the death penalty in the police officer's death.