Chenin Duclos and eight other bystanders were wounded by police gunfire, ricochets and fragments. Officers were engaged in a gunfight with a man suspected of gunning down a co-worker.
Duclos alleges the officers were grossly negligent.
The lawsuit says police should have taken steps to avoid the confrontation. It suggests they should have waited until he moved away from bystanders.
The shooting happened as thousands were on the streets surrounding the landmark on a bright August morning.
There was no immediate comment from city officials.
The lawsuit seeks unspecified damages. It was filed Tuesday in State Supreme Court in Manhattan.