NEW YORK (AP) — Some city residents wondered Tuesday if it’s time to pull the plug on the gaudy West Indian Day parade after three people, including a woman sitting outside her home, were shot to death just blocks from its route.

“I was saying to myself a while ago they probably should shut it down,” said Winston Thomas, a 66-year-old who moved from Jamaica to Brooklyn, site of the annual Caribbean-themed Labor Day parade, 40 years ago. “If you create this kind of atmosphere where you’re killing people all the time, it don’t make sense. … I stay away from it.”

Mayor Michael Bloomberg blamed illegal handguns for the shooting that killed three people and wounded two police officers near the parade route shortly after the parade ended Monday night, saying federal officials have not had the “courage” to take steps to control gun use.

Bullet fragments hit one police officer in the left arm and chest, and he was hospitalized but was expected to survive. Another officer was grazed by a bullet. Two gunmen were killed along with 56-year-old Denise Gay, who was shot while sitting on a stoop with her daughter just two doors down from the exchange of gunfire.

Bloomberg said Gay’s death was “a senseless murder and another painful reminder, I think, of what happens when elected officials in Washington fail to take the problem of illegal guns seriously.”

The Brooklyn block where Gay lived was cordoned off with police tape Tuesday. Neighbors said the area — a gentrifying slice of Crown Heights where hip coffee shops abut discount stores and West Indian bakeries — is generally safe.

“This is a very safe neighborhood,” resident Dennis McGreevy said. “This is one incident that happened here, that because it involves an innocent bystander and because it involves the police, has drawn a lot of news coverage.”

The gunshots rang out just after 9 p.m. Monday after the hours-long parade, which also was marred by fatal shootings in 2003 and 2005. Post-parade parties are common, but police wouldn’t say if Monday’s fatal shooting was related to the parade.

The shooting started as an exchange between two armed men, and when officers who had been assigned to parade duties arrived at the scene, they were fired upon and returned fire, police said.

The bloodshed was the main topic of conversation among neighborhood residents chatting in Tuesday’s light rain.

“A lady sitting on her stoop got killed for nothing,” Victor Hernandez said. “That could have been anybody. These guys with these guns, like Bloomberg said, they got to do something about these guns, man.”

Hernandez, a cook who’s on disability, said he enjoyed the parade but questioned why anyone would take a gun to it.

“What are you going to come here for with a gun to a parade? You’re looking for trouble,” he said. “We’re out here to have a good time, not to have violence.”

Charlotte Viola, a waitress, added, “It seems every time a crowd of people get together there’s some kind of problem. Always.”

Monday’s parade capped a particularly bloody holiday weekend in New York and included other outbursts of violence. Gunshots brought the festivities to a stop in spots, scattering the panicked crowd. Police said four people were shot and wounded along the Eastern Parkway parade route and a 15-year-old boy was grazed by a bullet nearby.

Parade organizers didn’t immediately return a call seeking comment Tuesday on what can be done to lessen the threat of violence at future parades.

Police Commissioner Raymond Kelly said that, despite the violence, ending the parade was unnecessary.

“I don’t think it’d be wise to close it down, but it’s just unfortunate that there seems to be every year some violence attended to it,” he said.

Also at the parade Monday, a City Council member and an aide to Public Advocate Bill de Blasio were briefly detained after getting into a confrontation with police.

Speaking Tuesday outside City Hall, Councilman Jumaane Williams and aide Kirsten John Foy said they were accosted by officers while walking along a blocked-off sidewalk.

The men, who are black, say they tried to show their city IDs to officers but their efforts were ignored. They say they wouldn’t have been stopped if they were white.

No charges were filed. A City Hall spokesman said police are conducting a thorough investigation into the incident.

Before the violence Monday, the parade thundered along Eastern Parkway, one of Brooklyn’s main thoroughfares, with its usual colorful, musical energy.

The parade celebrates the culture of the Caribbean islands and is one of the city’s largest outdoors events. Modeled on traditional Carnival festivities, it features spicy West Indian food and dancers wearing revealing feathered costumes.

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Associated Press writers Verena Dobnik and Karen Zraick contributed to this report.

Copyright 2011 The Associated Press.