(CNN) — School districts across the country are navigating how to reopen safely amid the deadly coronavirus pandemic, and the results of a new study could make those decisions more difficult.

Between 42% and 51% of all school employees in the US met the Centers for Disease Control and Prevention’s criteria for either having an increased risk or a potentially increased risk for Covid-19 infection, researchers with the Agency for Healthcare Research and Quality found.

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Underlying health conditions, such as obesity, diabetes and heart disease, and older age put people into the highest risk groups, according to the CDC.

“Among all adults with CDC risk factors for severe Covid-19, between 33.9 million and 44.2 million had direct or within-household connections to schools,” the researchers wrote.

Obesity and high blood pressure were the main factors that put school employees at higher risk of infection, the study reported. Men were more vulnerable to the virus compared to women, and Blacks were more at risk than Whites.

The analysis, released as a pre-print ahead of peer review by the journal Health Affairs on Thursday, used data collected between 2014 and 2017 to see how those most at risk for Covid-19 infection were connected to elementary and secondary schools either as employees or by living with staffers or school-aged children.

“Our results highlight the public health challenge that arises when the risk of school-related exposure is coupled with the potential for within-household transmission,” the researchers wrote.

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The study found low-skill support staff among school employees were more likely to be at increased risk of infection — more than 58% of them, compared to teachers and teaching assistants at 38%, or administrators and higher-skilled staff at 39%.

The analysis also found that 63% of school employees lived in homes where at least one adult was at high risk of contracting Covid-19; 59% percent of school-age children lived in households with at least one vulnerable adult, and high schoolers were more likely than elementary school children to live with an adult vulnerable to the coronavirus.

“While it is not surprising that the health issues of parents and other household members would increase as they and their children get older, this finding takes on special importance in the context of Covid-19, insofar as transmission risks also increase with child age,” the researchers said.

Just over 35% of American adults were either school employees or lived with someone connected to an elementary or secondary school or a school-age child, the study found.

The data reviewed predated the pandemic and doesn’t account for the tremendous changes that have occurred in employment, school attendance or household members, and there’s a likelihood the study undercounts the true number of those connected to a school and meeting the CDC risk guidelines for Covid-19.

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