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The “test-to-stay” policy that was intended to keep more U.S. students in school is on its way out in some states, a casualty of the monthslong Omicron wave that has left school districts struggling to find enough coronavirus tests to meet their needs.

Vermont and Massachusetts are turning away from tests that are given in school and sent to labs, in favor of rapid home tests.

“Test-to-stay,” endorsed by the Centers for Disease Control and Prevention in mid-December, was meant to allow students to stay in classrooms even if a close contact tested positive for the virus, and to restore stability for working parents. Instead of isolating at home, students who were exposed to the virus could keep going to school as long as they were asymptomatic, wore masks and regularly tested negative on rapid coronavirus tests.

The policy also replaced the default plan of quarantining entire classes when there was a positive case among the students.

At the time, the C.D.C. said that at least 12 states had policies that allowed test-to-stay programs: Illinois, Maine, Massachusetts, Michigan, Missouri, New Mexico, Oregon, Pennsylvania, Rhode Island, Utah, Vermont and Washington State. Some districts in other states also started their own programs.

Now Vermont is no longer relying on lab-based tests. In Massachusetts, public schools are being encouraged to concentrate on finding symptomatic people, to use rapid home tests, and to end contact tracing altogether. Gov. Charlie Baker announced last week that districts could follow the new policy as an alternative to test-and-stay.

Dr. Westyn Branch-Elliman, an associate professor at Harvard Medical School who advises the Massachusetts Department of Elementary and Secondary Education, said the state’s test-to-stay program, while previously “wildly successful,” no longer made sense. At-home testing of students would be the “wave of the future,” she added.

“Test-and-stay was a great program for the fall of 2021. But now it’s January 2022,” Dr. Branch-Elliman said. “We have vaccines, we have antivirals and we have Omicron. And all of those things mean we have to adjust our policies.”

Earlier this month, New York City replaced its previous policy of quarantining entire classes that were exposed to the virus with a new policy allowing asymptomatic students who test negative to remain in school. Public schools in the city are providing rapid at-home tests to students and employees who have symptoms or who were exposed to the virus in a classroom.

The Utah legislature suspended school testing requirements this month after districts said they were unsure whether they would have enough tests to comply. Utah’s state testing sites were overrun in mid-January with a surge of coronavirus cases, and Gov. Spencer Cox called on most…