The relationship between the National Institutes of Health and the National Football League has drawn congressional scrutiny in the wake of an ESPN report that claimed the league maintained veto power over millions in funding and “balked” at a brain injury study awarded to a neurologist critical of the NFL.

Letters from Democrats on the House Energy and Commerce Committee detailed on Thursday a request for the NIH to turn over communications between the agency and the league.

“We’re just trying to get to the bottom of it, because we do think that this research is very important,” said Rep. Frank Pallone Jr. (D-N.J.), who told The Post in a phone interview that the goal was simply to try to sort through conflicting statements.

One letter was sent to the NIH, and another went to the Foundation for the National Institutes of Health, a not-for-profit organization that Congress established to raise funds and create partnerships to support NIH’s mission. The letters were signed by Pallone, Gene Green (D-Tex.), Jan Schakowsky (D-Ill.), and Diana DeGette (D-Colo.). 

At the heart of the confusion is a $30 million donation the NFL made in 2012, a gift that was described as “unrestricted” at the time. ESPN’s “Outside the Lines” Dec. 22 report had suggested this wasn’t true; according to the report, the league maintained “veto power” — something the NFL and an FNIH spokeswoman denied after its publication.

ESPN reported the NFL had “backed out” of a research project focused on chronic traumatic encephalopathy, also known as CTE. At the time, the league pushed back on the report, calling it “not accurate.” The Foundation for the National Institutes of Health also said in a later statement that the league was “willing to contribute” to the study.

“The NFL did not pull funding from the BU study,” NFL spokesman Brian McCarthy wrote in an email to The Post at the time. “The NIH makes all funding decisions. The NFL has no ‘veto power’ as part of its unrestricted $30 million grant to NIH.”

The letter has asked for:

• Agreements between the league and NIH, the NFL and foundation, and the NIH and foundation, related to the NFL’s donation

• “Documents and communications” related to the donation that occurred between NFL employees and NIH employees, between NFL employees and FNIH employees, and between NIH employees and FNIH employees.

It also poses several questions, including whether anyone employed by or associated with the NFL used a threat of veto power over research funding. The NIH and FNIH were asked to turn over the information by Feb. 1, just days before the Super Bowl.

Rep. Fred Upton (R-Mich.), chairman of the House Energy and Commerce Committee, which has jurisdiction over health issues, announced a “broad review” of concussions in late December, though Pallone noted that the letter isn’t formally tied to that.

The CTE study in question is being led by Robert Stern, a Boston University researcher who apparently drew the league’s ire. Sources told ESPN that the league had “raised concerns about Stern’s objectivity, despite the merit review and a separate evaluation by a dozen high-level experts assembled by the NIH.”

The CTE research will continue but will not be funded from the money donated by the league.

“This study is important, and that’s why we’re trying to get to the bottom of this,” said Pallone, who in September requested a hearing about fantasy sports.

The budget bill that President Obama signed into law in December would increase the NIH’s budget by about $2 billion — from roughly $30 billion to $32 billion. About 10 percent of the budget supports projects by NIH scientists, mostly at labs in Bethesda. But more than 80 percent of the agency’s spending includes tens of thousands of grants that the NIH says support “more than 300,000 researchers at more than 2,500 universities, medical schools and other research institutions in every state around the world.”

Brady Dennis and Mike DeBonis contributed to this report.