Four other people, including two police officers, were injured in the fusillade. One of the bystanders, Cedric Simmons, who was hit in the shoulder and leg, agreed to a settlement. Two other suits stemming from that shooting are moving forward: one by another bystander, and the other by one of the men in the initial confrontation, Angel Alvarez, whom a grand jury declined to indict on gun charges.

The other settlements, in 2011, stemmed from a New Year’s Day shooting in Brownsville, Brooklyn, in 2003. Three officers pursuing an armed man, who was shooting at them, fired at him in front of a nightclub, as people waited in line around 3 a.m. In the cross-fire, two men were hit in the legs. “For the longest time, the police were saying that it was the perpetrator’s bullets that were in my clients’ body,” a lawyer for both men, Mark Shaevitz, said. When doctors later removed a bullet, he said, tests showed it came from a police gun.

Even so, Mr. Shaevitz said, the city moved for summary judgment. The case settled only after a judge warned the city that the trial would most likely go forward. Each man got $135,000.

Legal observers said the shooting near Times Square on Sept. 14 — in which the man being pursued did not have a weapon and there were visible crowds all around — presented a tougher set of facts that could force the city to soften its approach.

Nonetheless, the 2010 Court of Appeals decision presents a new hurdle for plaintiffs.

That decision came in a lawsuit filed by Tammy D. Johnson, a Harlem woman who was one of two bystanders shot as police officers exchanged gunfire with an armed robbery suspect in 2005. The other bystander, Garnold M. King, 78, who was wounded in the back, settled for $250,000.

In Ms. Johnson’s case, the panel ruled in a 4-to-3 decision that Police Department guidelines do not prohibit officers from opening fire when bystanders are around, but rather require that they exercise professional judgment that doing so will not “unnecessarily endanger innocent persons.”

None of the five officers testified to seeing pedestrians on the street before opening fire. In a dissent, three judges said that failure to observe bystanders presented enough of a question of police procedure for the lawsuit to go forward.