A damaged Capitol Hill police care is surrounded by crime scene tape after a car chase and shooting on Capitol Hill in Washington, Thursday, Oct. 3, 2013. WASHINGTON (AP) - A woman with a 1-year-old girl led Secret Service and police on a harrowing car chase from the White House past the Capitol Thursday, attempting to penetrate the security barriers at both national landmarks before she was shot to death, police said. The child was unhurt. "I'm pretty confident this was not an accident," said Metropolitan Police Chief Cathy Lanier. Still, Capitol Police said there appeared to be no terrorist link. The woman apparently was unarmed. Tourists, congressional staff and even some senators watched as a caravan of law enforcement vehicles chased a black Infiniti with Connecticut license plates down Constitution Avenue outside the Capitol. House and Senate lawmakers, inside debating how to end a government shutdown, briefly shuttered their chambers as Capitol Police shut down the building. The woman's car at one point had been surrounded by police cars and she managed to escape, careening around a traffic circle and past the north side of the Capitol. Video shot by a TV camerman showed police pointing firearms at her car before she rammed a Secret Service vehicle and continued driving. Lanier said police shot and killed her a block northeast of the historic building. One Secret Service member and a 23-year veteran of the Capitol Police were injured. Officials said they are in good condition and expected to recover. "This appears to be an isolated, singular matter, with, at this point, no nexus to terrorism," said Capitol Police Chief Kim Dine. Law-enforcement authorities identified the woman as Miriam Carey, 34, of Stamford, Conn. The authorities spoke on condition of anonymity because they were not authorized to divulge the information publicly. Stamford Mayor Michael Pavia said the FBI was executing a search warrant at a Stamford address in connection with the investigation. Police officers had cordoned off a condominium building and the surrounding neighborhood in the shoreline city. The pursuit began when the car sped onto a driveway leading to the White House, over a set of lowered barricades. When the driver couldn't get through a second barrier, she spun the car in the opposite direction, flipping a Secret Service officer over the hood of the car as she sped away, said B.J. Campbell, a tourist from Portland, Ore. Then the chase began. But it was going over the median and over the curb," said Matthew Coursen, who was watching from a cab window when the Infiniti sped by him. Police shot and killed the driver just outside the Hart Senate Office Building, where many senators have their offices. Dine said an officer took the child from the car to a hospital. She was not injured and was placed in protective custody, Capitol Police said. Rep. Michael McCaul, R-Texas, who said he was briefed by the Homeland Security Department, said he did not think the woman was armed. "There was no return fire," he said. A few senators between the Capitol and their office buildings said they heard the shots. "We heard three, four, five pops," said Sen. Bob Casey, D-Pa. Others witnessed the incident, too. Capitol Police on the plaza around the Capitol said they were working without pay as the result of the shutdown. Associated Press writers Adam Goldman, Mark Sherman, Philip Elliott, Jesse Holland, David Espo, Alan Fram, Eric Tucker, Brett Zongker, Donna Cassata and Henry C. Jackson in Washington, Michael Melia in Hartford, Conn., and John Christoffersen in Stamford, Conn., contributed to this report.