Police and the Obama administration remained tight-lipped on Friday over the handling of a car chase in Washington DC that ended when officers shot dead an unarmed woman in front of her one-year-old daughter.

Officials from the agencies involved in the incident declined to provide any explanation of their officers' actions, beyond praising them in glowing terms.

Officers from the secret service and Capitol police attempted to detain Miriam Carey, 34, after her car tried to breach a perimeter barrier close to the White House.

Video footage showed police appearing to corner her car before Carey managed to get away. Police gave chase and shot her dead around 1.7 miles from where the incident began. Carey's daughter was in the car at the time.

The White House refused to comment on the police's response to the incident. Spokesman Jay Carney refused to answer when asked how the secret service had handled the situation. Calls to the secret service's public information officer went unreturned.

The Washington Metropolitan Police department, which is leading the investigation, would not say whether officers involved in Carey's death had been suspended.

"I do not have that information. Those officers belong to different agencies. You'd have to reach out to them," MPD spokeswoman Saray Leon told the Guardian.

A spokesman for US Capitol police would not say whether it had suspended the officers responsible for Carey's death. "I can't say much about it right now because it is an ongoing investigation," the spokesman said. He said the Guardian should contact the MPD.

Police were hailed as "heroic" after thwarting the car chase. Congress afforded the officers a standing ovation as members lined up to praise their dedication and bravery. But it was unclear why police had shot the woman dead.

Leon said she could not confirm how many officers had fired their weapons, or how many rounds were discharged. "That's part of the investigation at this time, and we're not giving that information because it's ongoing," she said.

Washington Metropolitan Police chief Cathy Lanier told reporters on Thursday that the driver of the black Nissan had been killed.

"The suspect in the vehicle was struck by gunfire and has been pronounced dead," Lanier said.

"The United States secret service and Capitol police officers, from what I have seen so far in this investigation, acted heroically."

Two officers were injured, one from Capitol police and one from the secret service. One was reportedly hit by Carey's vehicle; the other crashed his police car into a barrier.

The chase began at around 2:15pm, when Carey's car attempted to pass a temporary barrier at 15th and E Streets, about half a mile from the Capitol. Secret service chief Ed Donovan said an officer was injured there, while others chased the woman along Pennsylvania Avenue towards the Capitol. They did not open fire.

Capitol police officers also gave chase, according to Lanier, and a number of police vehicles cornered Carey's car at Garfield Circle, in front of the Capitol Lawn. An officer was injured there after crashing his car.

Video footage filmed from the Capitol showed five law enforcement officials, guns drawn, approaching Carey's black Nissan Infiniti. The officers were within touching distance of the car, but the video showed the car reverse and drive off, making contact with a law enforcement vehicle on the way.

As Carey drove away, seven gunshots were heard. Police caught up with her about 300m away from the Capitol and shot her multiple times. Capitol police chief Kim Dine said "one of our officers rescued the child" after Carey had been killed. The one-year-old was taken to hospital.

The police gunfire caused a "shelter in place" notice to be called in the Capitol, with politicians forced to remain in the building. Tourists outside the building were ordered to the ground.

When the House of Representatives came to order after the lockdown ceased, House minority whip Steny Hoyer addressed his colleagues:

At the outset I know that I join the majority leader in expressing our gratitude to the Capitol police," Hoyer said. There followed a 30 second standing ovation. I know that that round of applause was heartfelt and deeply meant."

Law enforcement agencies appear to have begun briefing that Carey was mentally ill.

Within hours of her death, congressman Mike McCaul, the chairman of House homeland security committee, said he had been told by the FBI and secret service that investigators "think [Carey] had mental health issues". McCaul's comments were made to CNN just after 6:15pm – almost exactly four hours after the initial confrontation.

Carey's mother told ABC News that she had suffered from post-natal depression, but the incident shocked those who knew the 34-year-old.

"That's impossible. She works, she holds a job," Carey's sister, Amy Carey, told the Washington Post.

"She wouldn't be in DC. She was just in Connecticut two days ago. I spoke to her."

Donald Knowles, a friend, told CBS "she was all smiles" when he saw Carey a few days before she was killed, "like she didn't have a care in the world."

Barry Weiss, a dentist who employed Carey as an assistant, said he fired her in August 2012 after patients complained that she was rough, but remembered her as "an average employee".

"She started out pleasant. There were a few instances of her being headstrong but generally she was an average employee," he told NBC Connecticut. "She did her job and left at the end of the day."

Weiss said he was stunned when he was called by the FBI and the secret service on Thursday.

"Nothing would have led us to think she would have done this," he said.