Police in Washington could have avoided shooting dead a woman pursued by officers in a car chase that led to the lockdown of the Capitol this week, the driver's sister, former New York police sergeant Valarie Carey, said late on Friday.

The family of Miriam Carey, whose one-year-old daughter Erica was in the car with her during the encounter with police on Thursday, has said she suffered from post-partum depression.

Carey, 34, a resident of Stamford, Connecticut, tried to drive her black Infiniti coupe through a barrier near the White House, then sped toward Capitol Hill, leading police on a high-speed chase that ended when her car got stuck on a median and police shot her.

"My sister could have been any person traveling in our capital," Valarie Carey told reporters outside her Brooklyn home. "Deadly physical force was not the ultimate recourse and it didn't have to be."