Investigators believe that a Connecticut woman who was fatally shot by police Thursday after a car chase from the White House to the Capitol had grappled with mental illness and may have believed she was surreptitiously being monitored by President Obama.

Miriam Carey, 34, a dental hygienist living in Stamford, Conn., “may have thought President Obama was stalking her” when she steered her black Infiniti, with her 1-year-old daughter sitting in the back, onto some of the nation’s most highly guarded territory, according to a law enforcement official.

Carey had received a diagnosis of postpartum depression with psychosis, her sister Amy Carey-Jones said in a Friday interview on “Anderson Cooper 360°,” and had been treated with counseling and medication, but was reducing her use of medication under a doctor’s supervision. Carey-Jones said her sister “didn’t appear to be unstable.”

“We will never know what Miriam was thinking in those last hours before she died,” her sister told Cooper. “We can only speculate, and our real concern is why and were things done properly. Was there some other way that she could have been helped so that it didn’t end tragically?”

Rep. Michael McCaul (R-Tex.), chairman of the Homeland Security Committee, said the investigation has uncovered “a picture of a mentally disturbed woman.” Carey had been treated for schizophrenia, he said, but two of her sisters disputed his characterization.

This 2011 photo provided by Dr. Barry Weiss, from the website of Advanced Periodontics in Hamden, Conn., shows former employee Miriam Carey. (AP)

McCaul said her condition may have been exacerbated by a recent head injury and that her boyfriend had called police to say she believed her apartment was bugged and Obama was behind it. Carey’s sisters, however, said in their CNN interview that they had never heard her say anything of that nature. Valarie Carey called the boyfriend’s account “very questionable.”

For now, the biggest mystery is whether the incident that spun out 265 miles from Carey’s home was the culmination of a long, downward spiral or was sparked by some precipitating event.

Carey’s mother, Idella Carey, told ABC News that her daughter had not shown any violence in the past. She said she thought Miriam Carey was taking her toddler to a doctor’s appointment in Connecticut on Thursday.

Authorities are trying to trace Carey’s movements in Connecticut and Washington, where she apparently arrived only shortly before she approached a White House entrance and drove her car into a metal barricade just after 2 p.m. Thursday, then struck a uniformed Secret Service officer.

After speeding down Pennsylvania Avenue, she crashed at the Capitol grounds. Police scurried to carry the child to safety after her mother was shot several times.

In the New York City suburb of Stamford, about 100 law enforcement personnel from the U.S. Secret Service, FBI, Connecticut State Police and Stamford police searched Carey’s apartment in the Woodside Green complex overnight Thursday. They removed boxes, bags and at least one computer from the sprawling complex where a neighbor had seen Carey wheeling her daughter in a stroller.

The search involved hazardous-material teams, a bomb squad and a robot, Stamford Police Chief Jonathan Fontneau said. Under the assumption that something inside the apartment might pose a threat, police sent a robot through a window first and meticulously decontaminated people who went in and out of the unit, Fontneau said. In the end, they found just a “typical” first-floor two-bedroom apartment with “nothing out of the ordinary,” Fontneau said, and allowed evacuated residents to return to their units.

Until Thursday, the police chief said, Carey, too, “was nothing out of the ordinary that would draw attention to herself.”

Police had been called to the apartment once before, in December, but not for a criminal matter, Fontneau said. He did not have further details. A neighbor who declined to give his name said the tires were stolen from Carey’s car in the late spring or early summer and that Carey was somewhat upset at apartment officials about it.

“She was a little [irritated] about we’re paying all the taxes and common charges we pay and no security cameras,” the neighbor said. The encounter was the first and only time he met Carey. The neighbor said he found Carey fairly likable. “Very well-spoken,” he said. “She was obviously educated.”

People who were interviewed in the neighborhood Friday said they were still digesting the news that the woman at the center of the U.S. Capitol shooting was from their neighborhood. Charlie Clark, a 76-year-old crossing guard who chats regularly with Woodside residents, said that he was surprised that he did not recognize Carey’s photo when it was shown on television. “I kept looking at her, looking at her, I said, ‘See, that’s a beautiful lady,’ ” Clark said. “Hey, anything can happen. I’m just glad they didn’t kill that little baby.”

Mark Rosenbloom, who lives at Woodside, said he recognized photos of Carey’s car. It was always parked in an end spot in the complex parking lot and was especially well cleaned, he said. “You just notice sometimes cars that are shiny, especially when yours isn’t,” said Rosenbloom, 52. “I don’t think she wanted to get it scratched. Kept it in pretty good shape.”

Carey’s death also reverberated throughout several neighborhoods in Brooklyn, home to sisters Amy and Valarie, their mother, and other relatives.

On Thursday night, Carey’s friends and relatives congregated at the home of Valarie Carey, who lives in a two-story brick building on Marion Street in the Bushwick section of Brooklyn.

Family members traveled to the District on Friday to identify Miriam Carey’s body and later returned to Brooklyn where they spoke with reporters.

“My sister was not a criminal,” Valarie Carey said. “My sister did not deserve to have her life shortened at an early stage. She had aspirations, she had dreams . . . she has a family that loved her.”

Horwitz and Morello reported from Washington. Colum Lynch in New York and Paul Kane, Mary Pat Flaherty, Clarence Williams, Alice Crites and Jennifer Jenkins contributed to this report.