NORTH CHARLESTON, S.C. — The International Association of Machinists and Aerospace Workers (IAM) on Monday asked for an election so about 2,400 Boeing production workers here can decide whether they want union representation.

Union spokesman Frank Larkin said that the Machinists have petitioned the National Labor Relations Board and that under agency rules, 30 percent of the workers in a potential bargaining unit must sign cards that they want a vote.

“We are confident we have achieved the minimum requirement, and now the board will determine the exact number of people eligible to vote and then they will set and conduct the election,” he said.

South Carolina is a so-called right-to-work state where workers cannot be compelled to join a union or pay dues to a union as a condition of employment.

IAM representation of even a portion of Boeing workers in South Carolina would be seen as a big win for organized labor. Less than 4 percent of the state’s workforce is unionized, and Gov. Nikki Haley has vocally opposed a union at Boeing.

“We have a reputation internationally for being a state that doesn’t want unions,” the governor said during her State of the State address in January. “Now, that reputation and, even more importantly, a South Carolina company, are under attack.”

Mike Evans, a union organizer, said politicians should leave the unionization decision to Boeing workers.

“We expect Gov. Haley and her friends, who have no clue what it’s like to be a front-line production employee for Boeing, to keep their personal biases to themselves and remain neutral,” he said in a statement issued by the union.

The aeronautics giant on Monday immediately responded that a union is not in the best interests of the company, the workers or the state.

The exact number of those who signed cards to authorize a vote is not released, Larkin said. Boeing employs about 7,500 people in South Carolina.

Company spokeswoman Candy Eslinger said the petition to the NLRB includes production and maintenance workers at the assembly plant and the nearby Interiors Responsibility Center, which provides interior parts for the 787.

Larkin said he expects that about 2,400 workers will be eligible to vote.

Four years ago, shortly before the company opened the $750 million facility, the NLRB filed a complaint against Boeing alleging that the nonunion plant was built in retaliation against Washington state workers who went on strike.

The NLRB dropped the complaint later, after Boeing agreed that the 737 Max would be built in Washington.

Beverly Wyse, the vice president and general manager for Boeing South Carolina, said in a statement that South Carolina workers did what many said could not be done in opening the plant.

She said the union originally opposed the plant and now “the same union that tried to take our jobs and our work has already begun to divide our team.”

But Larkin said it’s important the workers be heard.

“Boeing has this ugly practice of pitting state against state and worker against worker, and a collective bargaining agreement can help level that playing field for workers,” he said.

The union has had members in the Charleston area before. It won the right to represent workers at Vought Aircraft Industries in 2007, a plant that Boeing later bought. Less than two years later, plant workers decided they did not want a union.