The report from the Office of the State Superintendent of Education suggested that the school’s record keeping was flawed and that students earlier had not provided the proper documents to prove residency.

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“In all of the cases from Duke Ellington School of the Arts described here, including those ultimately determined to be residents, the documentation on file at the school was inadequate to demonstrate meeting residency requirements,” the report reads.

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The Washington Post, based on a review of records provided by accused families, reported in October that a significant portion had been cleared — a conclusion supported by the city report.

The superintendent’s office announced in May that nearly 40 percent of the 570 students at the arts school were suspected of living outside the District without paying the tuition required of suburbanites who attend the city’s public schools. Some of the students suspected of fraud had been flagged for less clear-cut residency problems and told to provide more documents to verify their residency.

The report released this month updates the review of each of the 219 alleged enrollment fraud ­cases.

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About 5 percent admitted committing fraud, while 10 percent did not appeal the superintendent’s findings and have been deemed nonresidents.

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About 20 percent of the cases have been referred to the D.C. Office of Administrative Hearings because the families claim to be residents but the city remains unable to verify those assertions.

When the city made its announcement in May, families at the school quickly organized to repudiate the allegations. They successfully sued the city, arguing that it did not follow protocol when informing parents they were accused of residency fraud.

The families provided legal resources to one another, helping parents — particularly those from low-income households — fight the charges.

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On Monday, Greg Smith, an Ellington parent and lawyer who led the fight against the accusations, wrote a searing letter to the superintendent asking how the investigation went awry.

The Office of the State Superintendent of Education’s “false accusations have traumatized Ellington families, dried up Ellington’s fundraising, and damaged this school’s reputation. You owe Ellington, its students, teachers, funders and administrators — and the many families you falsely accused — a public apology,” Smith wrote in the letter to Superintendent Hanseul Kang. “Truly, how does a Government agency accuse citizens of fraud, and get it wrong more than half the time?”

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The superintendent’s office referred a request for comment to the mayor’s office, which did not immediately respond.

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The superintendent’s office has hired additional staff and improved training of registrars at schools. This academic year, the city will audit the residency verification documents for every Ellington student.