More and more American school districts have dropped mask mandates in recent weeks as coronavirus cases plunged across the United States. But they remain a subject of debate among some students and their parents, and a study released on Tuesday by the Centers for Disease Control and Prevention suggested that those mandates had helped protect children and teachers from the coronavirus last fall.

The study, examining public school districts in Arkansas from August to October as the Delta variant spread, found that districts with full mask requirements had 23 percent lower rates of the coronavirus among students and staff members than districts without the mandates.

It was not clear whether the same would have been true once the Delta variant was overtaken by Omicron, which is more contagious and spread rapidly among children and adults alike.

The C.D.C. has faced criticism from scientists in the past for overstating the benefits of school masking based on what some researchers have described as a flawed study out of Arizona. Some studies from abroad have also found that mask mandates were not associated with lower rates of the coronavirus in children.

But some scientists said that the latest C.D.C. study had steered clear of the most serious methodological problems and had strengthened the evidence for masks protecting some children from the coronavirus.

“It passes the smell test,” Louise-Anne McNutt, a former C.D.C. Epidemic Intelligence Service officer and an epidemiologist at the State University of New York at Albany, said of the study. “The estimates of the impact of masks are consistent with other studies that show masks have a modest, but important, reduction of SARS-CoV-2 transmission.”

The study compared coronavirus case rates among 233 Arkansas districts. About a third of the districts had full mask mandates, a fifth required masks only in certain settings or situations, and half had no mask policies.

It took into account staff and student vaccination rates and socioeconomic status. It also adjusted for coronavirus rates in the surrounding community — an attempt, the study’s authors said, to partly control for how much testing was happening in a given part of the state. Dr. McNutt, though, said that the study would have benefited from more details on statewide testing levels.

Districts with full mask mandates had lower coronavirus rates relative to the case rates in the surrounding community than districts without the mandates, the study found. And among roughly two dozen districts that put in place mask mandates in the middle of the study period, case rates afterward dropped more than would have been expected from changes in community case rates at the same time, the study said.

Partial masking policies did not show as strong an effect as full mask mandates.

The study did not account for schools’ prevention efforts beyond masking, like ventilating classrooms. Jonathan Ketcham, an economist specializing in health care at Arizona State University, said that could be an “important flaw in the study itself.”

Jason Abaluck, an economics professor at Yale University’s School of Management who helped lead a large trial on masking in Bangladesh, also cautioned that the schools with mask mandates could have differed from those without them in other ways, like adherence to distancing measures. He said that the study could have more closely matched nearby schools with different masking policies to study their effects.

But Dr. Abaluck said the C.D.C. study was an improvement on previous research.

“This study and the broader literature on masking suggests that in places where hospitalization and deaths are very high, the benefits of mask wearing in schools may be considerable,” he said.

Still, he noted that masks can cause discomfort and make it harder for children to communicate. “Figuring out how severe an outbreak has to be to warrant mask mandates in schools,” he said, “requires making best guesses about the costs, which remain highly uncertain given existing evidence.”