A woman with a year-old child attempted to crash through the White House perimeter with her car, then led Secret Service and police on a harrowing chase down Pennsylvania Avenue toward the Capitol before she was fatally shot Thursday in an incident that rattled nerves and tested Washington’s security during the government shutdown.

The midday drama sent bystanders scurrying for cover as gunshots rang out and heavily armed officers ran toward the scene where the woman’s car smashed a police cruiser before crashing. An officer pulled a child from the wreckage, apparently unharmed by the accident and gunfire. The child was taken to a hospital and was in protective custody Thursday night.

Police suggested that the incident, less than three weeks after a fatal shooting at the Navy Yard, showed the Washington security system worked perfectly even with the shutdown.

“Both at the White House and the Capitol, the security perimeters worked. They did exactly what they were supposed to do and they stopped a suspect from breaching the security perimeter in a vehicle at both locations,” Metropolitan Police Chief Cathy L. Lanier said at a late-afternoon briefing.

But questions were certain to persist, including what motivated the woman to begin the rampage, why Secret Service agents were unable to stop her car at the beginning of the incident and whether officers were justified in shooting a woman who apparently was unarmed and had a child inside her car.

U.S. Capitol Police Chief Kim Dine said officials did not think the incident was a case of terrorism.

“This appears to be an isolated, singular matter with — at this point — no nexus to terrorism,” he said. Chief Lanier also would not speculate on motive, saying only that it did “not appear in any way that this was an accident.”

The events occurred against the backdrop of a government shutdown that left 800,000 federal workers furloughed and a Homeland Security Department that is without a nominated secretary and several other top positions.

Authorities did not name the woman, but law enforcement officials confirmed the car was registered to a 34-year-old Connecticut woman and said police were searching a Stamford, Conn., home in connection with the investigation. The Associated Press, citing law-enforcement sources, identified the woman as Miriam Carey.

Officials said the incident began at about 2:12 p.m., when the woman struck temporary security fencing in a black Infiniti with Connecticut license plates and hit a uniformed Secret Service officer at an outer checkpoint for the White House. She sped down Pennsylvania Avenue, ramming her car into a Secret Service vehicle along the route.

The woman continued on to Garfield Circle — just outside the west entrance of the U.S. Capitol. A video taken at the scene shows officers with guns drawn approaching her stopped car. The car can be seen taking off as officers fired at her.

Police intercepted her again a few blocks away after she crashed her car in the 100 block of Maryland Avenue of Northeast, and opened fire on her for the final time.

One U.S. Capitol Police officer was injured when he crashed into a barrier during the pursuit. The officer, a 23-year-veteran, was airlifted to a hospital by the same U.S. Park Police chopper unit that two weeks earlier plucked victims off the roof of the Navy Yard during a shooting that left 13 dead, including the gunman.

The Capitol Police officer and the Secret Service officer were doing well Thursday night, officials said.

A spokesman for Senate Majority Leader Harry Reid said the Nevada Democrat called the injured Capitol Police officer and spoke with him in the hospital.

“Senator Reid asked the officer how he was doing, and the officer said he’s going to be fine,” Mr. Reid’s office said. “The officer said to Sen. Reid, ‘The only thing I do every day is to make sure you and everyone who works up here is safe.’”

Inside the Capitol, lawmakers offered a sustained bipartisan standing ovation after House Minority Whip Steny H. Hoyer, Maryland Democrat, expressed his gratitude to Capitol Police.

Outside the building, the fast-moving chase and the gunshots shook tourists and government workers alike.

Ryan Christensen of Idaho Falls, Idaho, said he was walking toward the west front of the Capitol when he saw the black car speed out of the roundabout.

“That’s when the shooting started,” he said. He and a friend took cover in the grass.

“We couldn’t really pay attention. We were trying to hide from stray bullets,” Mr. Christensen said.

Alan and Faith Silverman, visiting from Diamond Bar, Calif., were sitting on the East Lawn of the Capitol taking pictures when they heard six pops to their left.

“Then I heard what sounded like automatic gunfire, and I told my wife we should get up and move,” Mr. Silverman said.

Almost immediately, police ran across the lawn shouting at everyone to run if they were able, his wife said, impressed by the swift response. “We walked real fast — we’re too old to run,” she said.

Rep. Gerald E. Connolly, Virginia Democrat, and Rep. Matt Cartwright, Pennsylvania Democrat, were having a conversation on the balcony outside the House chamber when they heard two bursts of about seven or eight rounds of gunfire.

“We were like, ‘What is that?’ ” Mr. Connolly said. “I thought it was fireworks.”

Then officers waved for them to go inside.

At one point, an officer was crouched with a rifle to his shoulder, guarding visitors he had gathered and had crouching behind a stone wall near the Capitol.

A notice broadcast on the internal television system ordered employees to “close, lock and stay away from external doors and windows.”

Minutes after the alert was issued, police had barricaded off Constitution Avenue and shut down the grounds.

The House went into recess just about the time the alert was issued. The Senate remained in session for a while afterward but eventually went into recess.

At 3 p.m., police lifted the restrictions with a message to staffers: The incident has concluded. It is now safe to resume normal activities.”

The White House also briefly went on lockdown, and the pedestrian area on Pennsylvania Avenue was closed for a short time.

The White House said President Obama was briefed on the incident.

• Tom Howell Jr., Ben Wolfgang, Jeffrey Anderson and Stephen Dinan contributed to this report.

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