Many schools across the country have too much lead in their tap water, but most are not even testing for it, according to new research published Wednesday.

There’s no coherent policy for lead testing, and half of all U.S. students go to schools in states that do not even bother to have programs for testing drinking water for lead, the study found.

And even in those that do test for lead, more than 40 percent of schools turned up at least one sample with higher-than-recommended levels of lead in the water.

That could translate to millions of kids getting lead in the water they drink at school, the report from the Harvard School of Public Health and the Robert Wood Johnson Foundation found.

“Despite an uptick in awareness of and attention to the issue of lead in drinking water, many students in the U.S. attend public schools in states where not all taps are tested for lead,” the team wrote in their report.

A report last year from the federal Government Accountability Office, which found that 37 percent of school districts found elevated lead levels in students. The GAO found that 41 percent of school districts had not tested for lead within the past year.

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“All kids, no matter where they live, should have access to safe drinking water in school,” said Angie Cradock, of Harvard’s Prevention Research Center on Nutrition and Physical Activity, who led the study team. “Drinking water is important for helping kids grow up healthy, and water should be safe to drink.”

The research team looked at data from the 24 states that do have programs for lead testing in schools, plus Washington, D.C. Just 12 states provided usable results. Among them, 44 percent of the schools had at least one water sample with lead above the values allowed by local rules, which vary. And 12 percent of all the samples had higher-than-recommended lead levels.

There is no safe level of lead. Lead causes irreversible nerve damage and permanently damages the brains of babies and children. It can cause high blood pressure, among other problems, in adults. The Food and Drug Administration specifies bottled water should contain 5 parts per billion of lead or less.

Lead contamination in schools and in public drinking supplies is common across the U.S. Washington, D.C. had to shut off access to all its school drinking water after widespread contamination was found across the public water supply and in public schools there in 2003 and 2004. Flint, Michigan is still working to clean up its water supply after widespread contamination affected tens of thousands of people starting in 2014.

“Lead can enter drinking water when water service lines that bring water into a building or components of plumbing, such as solder or fixtures used in the school building, contain lead,” the report reads.

It can start leaching into water unexpectedly — for instance, after a new disinfection method is introduced or simply as pipes age.

But most schools are not regularly checking. “Most schools (89 percent) are not themselves subject to enforceable federal drinking water standards, including testing for lead, because they obtain their water from a public water supplier, typically a water district or a water utility company,” the report notes.

“Federal laws do regulate allowable lead content in drinking water among the 11 percent of schools that provide water for students via sources such as a well or cistern and operate as their own public water supply.”

Most testing programs are voluntary, and only 52 percent of states that have lead testing programs pay for them.

The programs often do not specify how many taps must be tested for lead, or how often they should be tested. “Schools that collected and tested water from a greater number of taps were also more likely to identify a sample with elevated lead concentrations,” the report read. That suggests that at least some schools cleared of lead contamination may in fact have tainted water, but testing was not extensive enough to show it.

And many states allowed lead levels in schools above the FDA’s limit for bottled water. “If all state programs used the action level that the FDA allows for bottled drinking water (i.e., 5 parts per billion) for lead content, there could be more than a doubling in the proportion of schools that would need to take steps in order to reduce the lead in their drinking water,” the report reads.

“More states should adopt programs to lower the lead content of school drinking water,” it concludes.