Washington - Police are reviewing the use of deadly force in the killing of a Connecticut woman who rammed a barricade at the White House, a shooting her family says was unjustified.

The investigation will reconstruct the car chase and shooting, which briefly put the U.S. Capitol on lockdown, and explore whether protocols were followed.

Senate Sergeant at Arms Terrance Gainer said he was confident the officers "did the best they could under the situation." Police guarding national landmarks must make fast decisions without the luxury of all the facts, especially when a threat is perceived, he said.

"The milieu under which we're operating at the United States Capitol and I suspect at the White House and at icons up in New York is an anti-terrorism approach," Gainer said Saturday, "and that is a difference with a huge, huge distinction."

U.S. Capitol Police Chief Kim Dine maintained that his officers acted "heroically" to protect the community.

Still, the family of 34-year-old Miriam Carey called the shooting unjustified, and some deadly force experts agree it merits scrutiny.

"We're still very confused as a family why she's not still alive," sister Amy Carey-Jones said in New York late Friday after traveling to Washington to identify the body. "I really feel like it's not justified, not justified." Another sister, retired New York City police officer Valarie Carey, said there was "no need for a gun to be used when there was no gunfire coming from the vehicle."

Secret Service agents and Capitol police officers fired shots during the Thursday afternoon encounter, which began when Carey - in a black Infiniti with her 1-year-old daughter - rammed a White House barricade and was pursued by police toward the Capitol in a high-speed chase.

D.C. Police Chief Cathy Lanier said she was confident after the shooting that Carey's actions were "not an accident," but the department's internal affairs division is investigating as part of standard protocol.

Carey struck a Secret Service agent with her car at the White House and reversed her vehicle into a police car, authorities say. A Capitol police officer was also injured. Both are expected to recover.

Experts in the use of deadly force said there were more questions than answers. Many departments direct their officers not to fire at moving vehicles - even if the driver is using the car as a weapon - or they permit it only under very limited circumstances. And experts wondered whether police should have relied on other options, such as establishing a roadblock, to diffuse the situation.

"I think the question we have to ask is, 'What threat did she cause?'" said Geoffrey Alpert, an expert on police use of force at the University of South Carolina. "What threat was she to the officers, to the public, to the politicians?"

Chuck Drago, a former Oviedo, Fla., police chief who now works as a police consultant, said he was concerned officers approached the vehicle on foot while the conflict was still unfolding. That kind of direct contact can elevate the tension of an already dangerous scenario and leave officers feeling vulnerable, he said.

"Their main concern should have been trying to keep that vehicle from moving, and then exposing themselves only adds to the danger and lessens their options in the long run," Drago said.

Authorities were investigating why Miriam Carey, who lived in Stamford, turned up in Washington on Thursday. A search warrant application for Carey's car seeks bullet fragments, maps or other documents pertaining to the White House, alcohol or drugs, "and/or evidence of a mechanical malfunction or lack thereof."

A federal law enforcement official said Friday that her mental health appeared to have been deteriorating in the last year and that she apparently was under the delusion the president was communicating with her. The official was briefed on the investigation but not authorized to discuss it publicly and spoke on condition of anonymity.

Her family said she had been suffering from postpartum depression with psychosis but was not dangerous.

But interviews with some of those who knew her suggested she was coming apart well before she loaded her daughter into the car for the 275-mile drive to Washington. She had suffered a head injury in a fall and had been fired as a dental hygienist about a year ago, her former employer said.

Carey's mother, Idella Carey, told ABC News that she began suffering from postpartum depression after giving birth in August 2012 and was hospitalized but had no history of violence.

After Carey rammed the barricades at the White House, police chased her down Constitution Avenue to the Capitol, where she was shot. At one point near the Capitol, police say, she stopped her car abruptly, drove over a median strip and put the vehicle into reverse and refused to stop. She was then shot.

Carey's daughter escaped serious injury and was taken into protective custody. The woman's family hasn't identified the child's father. Gainer said he hasn't seen any indication officers knew the child was in the car when they fired.

"There'll be lessons to be learned from this," Gainer said. "There'll be recommendations to be made about, "Could we have done this, or should we do that?"'

Carey's death comes less than three weeks after a shooting rampage in Washington that also involved an apparently unstable person.

On Sept. 16, gunman Aaron Alexis shot and killed 12 people at the Washington Navy Yard before being shot by police. Alexis, a defense industry employee and former Navy reservist, said in writings left behind that he was driven to kill by months of bombardment with electromagnetic waves.

Neumeister reported from New York. Associated Press writers John Christoffersen in Stamford, Lauran Neergaard in Washington, Michael Melia in Hartford and Jessica Hill in Hamden contributed to this report, along with AP researcher Barbara Sambriski in New York.