Chancellor Kaya Henderson and members of the D.C. Council’s education committee agreed Thursday that no one knows for sure whether D.C. schools’ 2008 test scores were inflated because of cheating.

It’s a question that has never been fully investigated, they said at a hearing devoted to examining test security in the city’s schools. It is also a question that appears unlikely to be resolved now.

Key council members and Mayor Vincent C. Gray (D) have said they do not plan to launch a full-scale investigation into the five-year-old tests. David A. Catania (I-At Large), chairman of the education committee, said the effort would be prohibitively labor-intensive for a council that can better spend its energy improving test security — and schools — in the future.

“We may never really know what happened in 2008,” Catania said.

Catania has introduced a bill that puts certain test-security protocols into law and would make cheating on D.C. tests — which are used to evaluate teachers and schools — illegal. That bill on Thursday drew support from Gray administration officials.

“We are focused on moving education in the District forward,” Gray spokesman Pedro Ribeiro said. “We’re confident that the systems and policies that we’ve put in place will help ensure the integrity of the test system.”

Council Chairman Phil Mendelson (D) agreed that it makes more sense to focus energy on improving education in a city where too many children are chronically truant and too few read on grade level.

But “there is a moral in this story,” Mendelson said, “and that is that while tests are important to measure progress, it’s counterproductive to put too much weight on the tests.”

Questions about cheating in the District have lingered for years and emerged again last week when journalist John Merrow unearthed a 2009 memo indicating that as many as 191 teachers at 70 schools might have been implicated in cheating on tests in 2008, during the tenure of former chancellor Michelle Rhee.

Rhee, who offered hefty bonuses to staff members in schools that made big test-score gains, now lobbies states around the country to adopt education policies she implemented in the District. She has said she doesn’t recall receiving the 2009 memo.

Henderson said under oath Thursday that she first became aware of that memo in January. The document — prepared by a consultant based on an analysis of wrong-to-right erasures on answer sheets — was based on incomplete information, she said.

Officials of the Office of the State Superintendent of Education told school officials not to investigate the 2008 scores further because the erasure analysis was inconclusive, Henderson said. Since then, the school system has taken additional steps to tighten security each year, she added, and multiple investigations have found no evidence of systematic cheating.

The document has raised questions about whether D.C. officials, including Inspector General Charles J. Willoughby, adequately investigated long-standing suspicions of cheating.

Willoughby conducted a probe that found no evidence of widespread cheating between 2009 and 2011. His investigation lasted 17 months and focused on one school, Noyes Elementary, even though Willoughby had a copy of the memo alleging wrongdoing at dozens of schools.

Council Member Kenyan R. McDuffie (D-Ward 5) questioned the inspector general Thursday about why he had limited his investigation to Noyes.

“We weren’t going on a fishing expedition,” Willoughby said, explaining that his investigators found no evidence of cheating at other schools while interviewing Noyes teachers, parents and students.

“I don’t think anybody expects you to go on a fishing expedition, but I do think folks expect you to conduct a thorough investigation,” McDuffie said. “Your investigation was woefully limited and relied too heavily on people who had an interest in not discovering cheating.”

McDuffie has requested permission to review Willoughby’s investigative file. The council member said in an interview that he does not intend to call for a new investigation, but he wants to ensure that future probes are thorough enough to inspire public confidence.

There are still questions about whether city officials are aggressive enough about investigating cheating now. The Office of the State Superintendent of Education released a report last week showing that teachers in 18 classrooms had cheated on 2012 exams, “proof that 99.4 percent [of teachers] are following the rules,” according to a news release.

Some said the office’s review was too lax. Classrooms were fully investigated only when they met two of four criteria. That amounted to a 41 classrooms, a tiny fraction of the 2,688 where tests were administered.