MISSION, Kan. — Children are having their noses swabbed or saliva sampled at school to test for the coronavirus in cities such as Baltimore, New York and Chicago. In other parts of the U.S., school districts are reluctant to check even students showing signs of illness for COVID-19.

Education and health officials around the country have taken different approaches to testing students and staff members – and widely varying positions or whether to test them at all as more children give up virtual classrooms for in-person learning. Some states have rejected their share of the billions of dollars the Biden administration made available for conducting virus tests in schools.

Officials in districts that have embraced testing describe it as an important tool for making sure schools reopen safely and infections remain under control. They note that the virus might otherwise elude detection since young people with the virus often are asymptomatic and most teachers have been vaccinated.

But many school administrators and families, weary of pandemic-related disruptions, see little benefit in screening children, who tend not to become as sick from COVID-19 as adults. Meanwhile, each positive test that turns up at a school can trigger quarantine orders that force students back into learning from home.

In Nebraska, Superintendent Bryce Jorgenson said he doubts parents with children in the Southern Valley Public School District would embrace school-based virus tests. His rural, 370-student district eliminated its mandatory mask policy in March.

“I can tell you right now, I would say that not just in our district, but in many districts around, there is not an appetite for that at all,” he said of ongoing screening. “I don’t know as a leader, too, if I want to get into testing kids because we don’t test kids for any other virus, really.”

Elected officials in Iowa and Idaho made their opinions known by turning down millions in federal aid for voluntary COVID-19 testing in schools.

“Here’s your $95 million back,” Iowa Gov. Kim Reynolds, a Republican, declared on Fox News after commenting that in her view, President Biden “thinks that COVID just started.”

In Idaho, the state House of Representatives rejected $40.3 million in offered funding.

“Schools are not medical facilities, and we shouldn’t want to place that responsibility and liability on our schools,” Republican state Rep. Tammy Nichols said in an email. “That is why we have medical facilities and staff who are licensed, certified and insured to handle those things.”

Experts are divided about how worthwhile it is to test for the coronavirus inside schools as more people are vaccinated and confirmed cases decline.

Joshua Salomon, a professor of medicine at Stanford University who supports screening students, said the procedure could help curb outbreaks involving more contagious variants.

“Basically, it gives you an insurance policy against things we may not be able to anticipate,” Salomon said. “The virus has really kind of caught us off guard in a few instances.”

Students line up to enter Christa McAuliffe School in Jersey City, N.J., at the end of April. Seth Wenig/Associated Press

But Dr. Monica Gandhi, a professor of medicine at the University of California, San Francisco, said the nation’s vaccination program makes the tests less useful because immunized individuals are so much less likely to get infected. At the same time, she said, false positives in school settings carry significant consequences when they cause a return to online learning.

Screening tests have played a key role in reopening plans for schools in New York City and liberal-leaning states like California and Massachusetts.

Some districts, like Baltimore City Public Schools, use so-called pooled testing methods that combine multiple samples from students in kindergarten to eighth grade; a positive result leads to everyone in the pool being quarantined. The district is using individual saliva-based PCR tests to screen its high school students.

“By doing this screening testing, you can actually catch the cases early, and that is really effective at preventing transmission,” Cleo Hirsch, who oversees the testing in Baltimore’s public schools, said.

In Chicago, surveillance testing for COVID-19 was part of the district’s reopening agreement with the teachers union. For elementary students who are at least 10, the district tests a percentage at random, focusing on zip codes with the most confirmed COVID-19 cases. The district tests a sampling of high school students citywide. The tests require parental consent.

In Massachusetts, which also relies on pooled testing, the collected data indicates a positivity rate within schools of 2 cases for every 1,000 people, said Russell Johnston, a senior associate commissioner at the state’s Department of Elementary and Secondary Education.

“That just again gives us enormous confidence in the mitigation strategies that we have available in the schools,” he said.

Oregon is beginning to pilot testing of unvaccinated school employees and plans to expand the health surveillance effort to children attending overnight summer camp before deciding how to proceed in the fall. Some school administrators have expressed trepidation about adding surveillance testing, state epidemiologist Dr. Dean Sidelinger said.

“COVID has added 12 new challenges every hour for them on top of everything else they were already burdened with,” Sidelinger said. “So many of them just kind of, I think instinctively, said, ‘No, you cannot ask us to do another thing.’”

In Minnesota, the 8,500-student Edina Public Schools has quarantined hundreds of close contacts of students with positive results. The district began a “Test The Nest” surveillance program at its high school and middle schools in mid-March in an attempt to identify individuals without symptoms who are carrying the virus, spokeswoman Mary Woitte said.

But Nicole Schnell, of the group Edina Parents 4 Progress, opposes the expanded testing, saying a single positive case can lead to massive disruptions.

Schnell said her daughters, age 15 and 18, spent two weeks quarantined in the fall and another two weeks in the spring despite testing negative because they were considered close contacts of people who were infected. Her 17-year-old son decided to keep attending classes virtually because he didn’t want to risk a potential exposure that might force him to miss the spring baseball season.

“I have seen firsthand effects of keeping kids out of society,” Schnell said, adding that one of her children was diagnosed with depression after being quarantined. “We are not just talking about out of school. We are talking about out of any sport that they play, out of any activity, out of anything outside, out of seeing their friends, because of a potential positive exposure.”