Justice holds in her right hand an unsheathed sword, in her left the traditional balance. She's often shown blindfolded (to symbolize fair and equal administration of justice to all), but a number of statues exist where her eyes are wide open; this is one of them.
In August 1858, New York celebrated the completion of a transatlantic cable (which failed in September, and was not reconnected until 1866) with a fireworks display so exuberant that the cupola of City Hall caught fire. A blindfolded Justice crashed down through the burning roof. A new wooden Justice soon rotted, to be replaced in 1887 by this one of painted copper. The current statue was mass-produced in Ohio from the work of an anonymous artist.
Literally and metaphorically, Justice had her back turned on the Manhattan courthouse where Martha Stewart was convicted in 2004. Ms. Stewart may or may not have acted illegally. But the government's choice to spend so much time and money investigating and prosecuting her - rather than people who are clearly a threat to lives and property - demonstrates priorities so misplaced that that they must be based ultimately on a profoundly flawed idea of justice.
Food for thought on justice:
Justice consists first not in condemning, but in admiring - and then in expressing one's admiration explicitly and in fighting for those one admires. It consists first in acknowledging the good; intellectually, in reaching an objective moral verdict; then existentially, in defending the good - speaking out, making one's verdict known, championing publicly the men who are rational .... What counts in life are the men who support life. They are the men who struggle unremittingly, often heroically, to achieve values. They are the Atlases whom mankind needs desperately, and who in turn desperately need the recognition - specifically, the moral recognition - to which they are entitled. They need to feel, while carrying the world on their shoulders, that they are living in a human society and that the burden is worth carrying." - Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand, pp. 284-5 (paperback).
On the City Hall Justice, see Burrows & Wallace, Gotham p. 676, and Gayle & Cohen, The Art Commission and the Municipal Art Society Guide to Manhattan’s Outdoor Sculpturepp. 43-44.