The last of seven bodies was pulled from the rubble at the site of a crane collapse in Manhattan, police said today.

Six construction workers and a woman in town for St. Patrick’s Day were killed Saturday when the 19-story crane broke away from an apartment tower under construction and toppled like a tree onto buildings as far as a block away. The last three bodies were found today.

A preliminary investigation found that the crane toppled when a steel collar used to tie the crane to the side of the building fell as workers attempted to install it, damaging a lower steel collar that supported the crane. With the elimination of that support, the counter-weights at the top of the crane’s tower caused it to fall, investigators said.

As rescue workers dug through the rubble, the neighborhood just blocks from the United Nations struggled to return to normal. One lane of Second Avenue reopened to traffic, and many stores and bars were open for business.

The manager of an Irish bar noted how fortunate it was that the accident didn’t happen today, when hundreds of thousands of people thronged nearby Fifth Avenue for the annual St. Patrick’s Day parade.

“If it happened today there would be carnage,” a Jamison’s Pub manager, Michael Mullooly, said, referring to the half dozen or so Irish bars in the neighborhood that typically attract large crowds on St. Patrick’s Day.

Two people — a woman and a construction worker — were believed to be inside the four-story brick town house that was completely demolished when the crane came crashing down. The blocks around the construction site consist mostly of low-rise residential buildings but in recent years developers have erected a number of big condo towers, sparking concerns among residents about the pace of development.

The missing woman had come from Miami to celebrate St. Patrick’s Day and to visit a friend who lived in the town house, the owner of Fubar, a saloon on the ground floor of the town house, John LaGreco, said. The woman was in her friend’s second-floor apartment at the time of the accident and hasn’t been heard from since, he said. Her friend was rescued.

Twenty-four others were injured, including 11 first responders, Mayor Bloomberg said. Eight people remained hospitalized, officials said.

Officials were investigating whether human or mechanical error led to the construction-site accident, which the mayor described as among the city’s worst. City officials said the broken crane passed inspection Friday.

The accident occurred while workers were adding tower sections to extend the crane upwards, an operation known as “jumping” the crane, according to investigators with the Office of Emergency Management.

While crews were jumping the crane to the 18th floor, the steel collar, which wrapped around the mast of the crane and is used to tie the crane to the side of the building, fell as workers attempted to install it.

When the steel collar fell, it damaged a lower steel collar, installed at the 9th floor. The collar installed at the 9th floor served as a major anchor securing the tower crane to the building under construction.

With the elimination of the support provided by the steel collar at the 9th floor, the counter-weights at the top of the crane’s tower caused the entire crane to topple southward.

The city had answered 38 complaints and issued more than a dozen violations in the past 27 months to the construction site where the 43-story high-rise condominium was going up. None of the violations was related to the crane, Bloomberg said.

On Sunday, the Reliance Construction Group, the project’s contractor, released a statement expressing sympathy to the families of the dead and injured and said it was cooperating with government investigators.

Four of the workers killed in the accident were identified as Wayne Bleidner, 51, of Pelham; Brad Cohen, 54, of Farmingdale; Anthony Mazza, 39; and Aaron Stephens, 45, of New York City, police said yesterday. The three people whose bodies were found today had not yet been identified.

About 250 cranes operate in the city on any given day, and the accident shouldn’t alarm New Yorkers living near high-rise construction sites, the mayor said. “This is a very tragic but also a very rare occurrence,” he said.

But neighborhood residents and a Manhattan borough official raised concerns about city inspections at the apartment tower.

A retired ironworker, Kerry Walker, who with his wife lived in the top-floor apartment of the four-story town house and left minutes before the collapse, had complained that the crane appeared dangerously unstable, his stepson said.

“He knows all about cranes and said this one had no braces, everything was too minimal,” the stepson, John Viscardi said. “He told one friend on the phone that ‘if you don’t hear from me, it’s because the crane fell on my house.'”