Did you all see the video?
It seems that an Arabic TV station were filming a placard-holder in the park in front of the Capitol (can't read the sign, presumably a goverment shutdown message) when all of a sudden the drama unfolds just down the path from them.
The full vid at CBS goes on for another few minutes, and shows the cameraman and reporter running up by the Capitol Building itself as armed police usher people away from the scene.
http://www.cbsnews.com/8301-250_162-57605915/woman-dead-after-chaotic-capitol-car-chase/
*opens Google Maps*
That puts it at the US Treasury building, maybe the nearest she could get by unblocked road?
Makes sense, that's the main thoroughfare between the two.
The vid shows a monument and circle in the background, so after checking street view, I've corroborated that the start of the vid took place at the President James Garfield Memorial, just near the Capitol Reflecting Pool.
After escaping the police, you then see her drive off, and towards the end of the vid, she's at another circle, leading the police a merry chase round and round the roundabout. This was (ironically under the circumstances) the monument called the Peace Circle.
End of investigation.