Kansas City, Mo. ? Members of the largest union at Boeing Co.’s commercial aircraft division in Wichita on Tuesday turned down a labor agreement that Onex Corp. said was vital in its plan to buy the plant.

Members of the International Association of Machinists and Aerospace Workers rejected the proposal by 57 percent, said Steve Rooney, Lodge 70 president. The union declined to say how many of its members – the union represents 5,300 workers – at the plant voted Tuesday.

“The membership has spoken,” Rooney said. “The next step is Onex’s.”

In a written statement, Nigel Wright, Onex’s managing director, said he was “obviously disappointed” in the vote and thanked those who had supported it.

“We are reviewing our options and want to give them careful consideration before making a determination about our next steps,” Wright said.

The Canadian investment firm previously had said it would walk away from the deal if the union rejected the agreement.

Union members had been critical of the proposal, which required a 10 percent pay cut and other concessions.

Members also were angry after Onex sent notices to 800 employees at the plant during the weekend, notifying them that they would not be rehired and telling them not to come into work Monday. Union officials said they didn’t know how many of those 800 workers belonged to the union.

While it’s possible that Onex could decide to return to the negotiating table, one expert said the union may have made an error in calling Onex’s bluff.

William Alderman, president of Alderman & Co., an aerospace and defense investment banking firm in South Norwalk, Conn., said Onex may find Wichita too hostile to carry on negotiations, especially as Onex is not trying to become a major player in aviation.

“A strategic buyer … is much more likely to say, ‘I’m willing to bear with this pain,’ ” Alderman said. “A financial buyer, like Onex, is more likely to say, ‘There are other places to put my money.’ Onex is much more likely to walk.”

If that happens, Chicago-based Boeing has said it would have to downsize the plant, either by selling the business piecemeal or outsourcing jobs.