By the time the chase ended, dozens of shots had been fired and two officers were injured. The child was unharmed.
Coming a little more than two weeks after the Washington Navy Yard shooting, the episode unnerved a city already feeling the tensions between the White House and Congressional Republicans that have ground the federal government to a halt and kept thousands of people home from work.
The Capitol was locked down for a half-hour during the chase and shooting. Afterward, House Republicans and Democrats took to the floor to praise the response of the Capitol Police.
The authorities identified the woman as Miriam Carey, 34, a dental hygienist from Stamford, Conn. They had difficulty identifying her because of the extent of her injuries.
The Stamford police roped off and evacuated Ms. Carey’s condominium complex Thursday afternoon and bomb units stood by. F.B.I. agents were also looking to interview the woman’s relatives in Brooklyn. Neighbors in Connecticut said Ms. Carey had a child, but it was unclear if the toddler in the car was hers.
Dr. Brian L. Evans, a periodontist in Hamden, Conn., for whom Ms. Carey had worked until about a year ago, said that he believed that she had suffered a significant head injury sometime during the year she was employed by him.
He described Ms. Carey as having “a bit of a temper,” but “nothing unusual, nothing that would ever lead us to think she would ever do anything like this.”
Representative Juan Vargas of California said he was walking back toward the Capitol when he heard several loud bangs, which he initially thought might be a car backfiring.
“I heard ‘pop, pop,’ and honestly I didn’t think anything of it,” he said. Then, he said he saw a police officer charging for him: “I was wondering what’s going on, why is this guy coming at me like a maniac? What’s the deal here? I didn’t understand what had happened.”
When the officer noticed that Mr. Vargas was wearing one of the red-and-gold pins that are issued to House members, he told the congressman to remove it because he could be a target.
The chase began at 2:12 p.m. when Ms. Carey, who was driving a black two-door Infiniti with Connecticut plates, attempted to ram through a White House check point at 15th and E Streets Northwest.
“The guys ran to try to stop her, and she wasn’t going to slow down, so they jumped aside,” said B. J. Campbell, a tourist from Portland, Ore., who was standing near the White House. “One of the guys grabbed one of those little metal fence sections and shoved it in front of her, across the driveway. She hit the brakes slightly and tried to get around it on the right, but the guy shoved it in front of her again, to try to keep her in.”
Mr. Campbell said the woman “hit the gas, ran over the barricade” and hit the officer, who flipped onto the hood of the car and “rolled off into the gutter.”
“After she ran him down, she gunned it, and she just went screaming down Pennsylvania Avenue,” he said. “They were busy calling on their phones, on the radios. It was like poking a hornet nest. There were guys everywhere. I didn’t see anyone with their guns out, but they were sure busy.”
Despite attempts by uniformed Secret Service officers to get her to pull over, Ms. Carey sped down Pennsylvania Avenue toward the Capitol at as much as 80 miles per hour and drove through several red lights, law enforcement officials said.
Several minutes later, officers appeared to have the woman cornered in front of the western side of the Capitol facing the National Mall. But as officers, with their weapons drawn, approached Ms. Carey’s car, she rammed it into reverse.
Officers tried to dodge out of the way, but the Infiniti struck a police car and raced up Constitution Avenue, where it crashed into a barrier. Ms. Carey, who was unarmed, got out of the car and was shot, although she also may have been hit while she was in the Infiniti.
The authorities took her to a hospital and she was pronounced dead.
There was panic inside the Capitol campus as it became clear that the police were mobilizing for a security threat. The loud buzzers were a jarring sound in a city still on edge from the shootings last month at the Washington Navy Yard that killed 12 people. Police officers ran through corridors, their semiautomatic rifles drawn. They quickly sealed off the entrances to hallways and instructed people to remain in place.
During the lockdown, the police permitted some members of Congress to walk through the underground tunnel that connects the Capitol to the Senate office buildings.
At one point, Representative Darrell Issa, Republican of California, snapped at the police guarding the entrance to the tunnel, “Let me past, I am going through,” as he marched back toward the Capitol.
Edmund Ofori-Attah and his wife, both missionaries from Togo, were about to tour the Dirksen Senate Office Building when the Infiniti sped by on Constitution Avenue pursued by two police cars. The car hit a barricade as it tried to make a left turn at a police checkpoint, and five to six gunshots were fired, he said.
“We just dropped to the ground,” Mr. Ofori-Attah said. “I didn’t want to get hit.”
When Mr. Ofori-Attah got up a few minutes later, he said he saw the police remove the child.
Brian Johnson of the American Petroleum Institute was parked at the Capitol, when he heard shots. “My heart just dropped, and we just ran behind my car,” he said.