An at-large voting system for electing members to the East Ramapo school board — long dominated by Orthodox Jews whose children attend private yeshivas — has prevented public school parents who are largely black and Latino from electing candidates of their choice, according to a lawsuit filed on Thursday by the New York Civil Liberties Union.

“What we have in East Ramapo is a common case of disenfranchisement of minority voters in the extreme,” said Donna Lieberman, executive director of the New York A.C.L.U. “The system allowed for the white community that does not send its children to public school to hijack the school board.”

The complaint, filed in the United States District Court for the Southern District of New York against the school district and the State Department of Education, argues that the election system violates the federal Voting Rights Act by denying “minority citizens an equal opportunity to have a voice in the future of their community’s public schools.”

A “toxic combination of an at-large elections system and racially polarized voting,” the lawyers say, has made it seemingly impossible for candidates backed by minority voters to win “even a single contested election in the past decade.”

Plaintiffs in the case — the Spring Valley branch of the National Association for the Advancement of Colored People, parents of public school students, district residents and candidates who have run unsuccessfully for a seat on the board — are calling for the current system to be replaced with a ward election system that would give minorities “an equal opportunity” to elect their favored candidates.

Orthodox Jews have represented a majority of the nine-member board since 2005. Under the at-large election system a white voting bloc “effectively shut out advocates for the public school community,” the lawsuit claims.

The lawsuit is the latest twist in a years long, ongoing battle between the board, which has been accused of diverting funds from local public schools to Orthodox Jewish students in private schools, and black and Latino residents in the district. Of the nearly 35,500 students in the district, 76 percent attend private schools, mostly yeshivas. Black and Latino students represent more than 90 percent of the district’s public school population.

The school district in East Ramapo, located roughly an hour north of Manhattan in Rockland County, was once well-regarded, but in recent years has become one of the poorest performing districts in the county, according to the lawsuit.

A fiscal monitor was appointed by the state Education Department to investigate the district’s finances in 2014 after years of severe cuts including the elimination of 445 positions and a reduction of full-day kindergarten. Athletic, arts and music programs, and extracurricular activities were also gutted while the private schools received a boost in public funding for transportation and special education, and taxes were cut.

A state investigator found that cuts were made with no meaningful effort “to distribute the pain of deep budget cuts fairly among public and private schools.”

The board also lacked transparency and oversight, and often spent a majority of its meetings in executive sessions.

The state has continued to appoint monitors, including a team led by Dennis M. Walcott, a former New York City schools chancellor under Mayor Michael R. Bloomberg, to the district leading to some money being restored. But public school advocates and city officials say wider representation on the board is sorely needed.

“I do think a case could be made that the majority can’t just trample over the rights of the minority here,” said Assemblyman Kenneth P. Zebrowski, a Democrat from Rockland County. “At what point do we get to that and say that you are not fulfilling the core mission of the school district.”

At-large voting in school board elections has been challenged in districts in other states in recent years. In New York, all school districts excluding the Buffalo school district use at-large voting to elect board members, according to Timothy Kreamer, executive director of the New York State School Boards Association.

Yehuda Weissmandl, president of the East Ramapo school board, declined to address the allegations in the lawsuit. He said he had not reviewed the complaint, but said it “will cost students at the district programs and opportunities” because money from the budget will be used to fight the lawsuit.

Mr. Weissmandl said the board did not make the election rules.

Eric Goodwin, one of the plaintiffs in the case, moved to Nanuet, which is part of the East Ramapo district, in 2011 in search of a “better life” for himself and his family, including his 12-year-old son who had been a student in a Harlem private school. Mr. Goodwin placed his son in public school because he believed that in the suburbs it would be equivalent to private schools. But he quickly learned that he was wrong.

His child’s music class did not have enough instruments for each student so Mr. Goodwin said he spent $35 a month for a year to rent a clarinet for his son. The textbooks were dated.

“I just want my child to get the same opportunities as everyone else,” he said.

Mr. Goodwin decided to run for a seat on the board with the idea that maybe he could make a difference as a member. He lost to a candidate supported by the private school community.

“A lot of people were disenfranchised and discouraged from running,” he said. “People would say, ‘It’s not going to change. They won’t give up that power.’”