Correction: A previous version of this article incorrectly stated that Harmony Public Schools students in Texas fell short of the national average on math and reading portions of the 2012 SAT college-entrance exam. While Harmony students fell short of the national average for the combined math and reading portions of the exam, they exceeded the national average for math and fell short of it for reading. This version has been corrected.

The largest charter-school operator in Texas, an organization with a solid academic record but lingering allegations of connections to a controversial Muslim cleric, is seeking to expand to the District next year.

The D.C. Public Charter School Board is scheduled to vote Monday on whether Harmony Public Schools should be allowed to open a science- and math-focused school in Washington in fall 2014. Harmony runs 40 Texas charter schools that enroll more than 25,000 students.

Founded in 2000 by a group of Turkish-born immigrants, Harmony has won acclaim for its performance in Texas, including from the Obama administration, which awarded Harmony $30 million last year through the Race to the Top grant competition.

It serves a majority-minority student population, more than half of which come from low-income families. Superintendent Soner Tarim said his organization can fill a need in the nation’s capital for science, technology, engineering and math — or STEM — education.

“We feel that STEM is right for our nation’s future,” Tarim told the charter board in October. “Opening a school here will create a model for the entire nation.”

All but one of Harmony’s schools met Texas state performance standards in 2013, and officials say the schools have a 100 percent graduation and college-acceptance rate. Although Harmony high school students fell short of the national average for combined math and reading portions of the 2012 SAT college-entrance exam — with math scores that exceeded the national average and reading scores that were below the national average — Harmony students outscored the Texas state average in both categories.

But Harmony’s business practices have drawn scrutiny. A 2011 investigation published in the New York Times raised questions about whether the charter network has used taxpayer dollars to benefit a social and religious movement led by Fethullah Gulen, an influential Muslim preacher from Turkey who now lives in Pennsylvania.

Tarim denied any connection with Gulen. “I am not a follower of anybody,” he said. “Harmony has no affiliation with any religious organization, including the Gulen movement.”

Sound financial management and responsible use of taxpayer dollars are key issues for the city charter board as it evaluates applications, especially given recent allegations of a multimillion-dollar self-dealing scheme at the District’s oldest charter school.

“I think it’s our obligation to be savvy customers on behalf of D.C. kids,” said Don Soifer, a member of the charter board who visited a Harmony school in Texas and found it to be well-organized and have an impressive level of instruction. “It’s important to sort out the legitimate questions from what might just be hearsay. And where there are legitimate questions, to find answers.”

Harmony is one of two organizations seeking a new charter under a fast-track process that allows experienced school operators to open a year ahead of the regular timetable.

The other applicant is Harlem-based Democracy Prep, which has proposed opening an elementary school for 650 children. Democracy Prep has nine campuses in New York and New Jersey and is known for its strict “no excuses” approach to educating inner-city children.

The D.C. charter board hired the National Association of Charter School Authorizers to review the records of applicants, according to spokeswoman Theola Labbé-DeBose, who said that the reviews are “deliberative” and therefore not required to be released to the public.

Harmony’s application has drawn more attention. Critics have written letters urging the board to reject it, alleging possible ties between the school and Gulen.

More than 120 U.S. charter schools are operated by Turkish-born immigrants, and critics have alleged that many have connections to Gulen. People familiar with the schools say they do not teach religion.

The 2011 New York Times report about Harmony said that nearly all Harmony contracts awarded between 2009 and 2011 went to Turkish-owned firms, even when non-Turkish firms put in lower bids.

Tarim, who is leading the effort to expand to the District, said that Harmony has always abided by the law and that critics have been fueled by xenophobia. “We are treated as an outsider,” he said, calling the report by the Times unfair: “I strongly felt we were mistreated.”

Tarim said that Harmony has rejected the lowest bidder for a contract only twice, and for good reasons. In one case, the low bidder wouldn’t have been able to complete a school-construction project before the first day of classes. In the other, the low bidder on a food-service contract was offering frozen meals, and Harmony schools had no ovens.

The Texas Legislature investigated Harmony after the report by the New York Times, but legislative staff workers said the investigation ended without a written report.

In 2012, the Texas state education agency released an audit showing that Harmony failed to properly document its use of $186,000 in federal funds, or about one-third of the dollars auditors examined for the fiscal year ending in August 2010. “Inadequate internal controls . . . resulted in the misuse of federal funds,” the audit said.

Harmony repaid the $186,000, according to a spokeswoman for the Texas education agency. But Harmony officials maintain that they did nothing wrong, saying that the audit’s findings were the result of a dispute over how to properly document the expenditure of federal grant funds.