Prince George's County residents participate in a Maryland Health Connection enrollment event at Laurel High School on October 5, 2013. (Marvin Joseph/The Washington Post)

A federal audit of Maryland’s once-troubled health-insurance exchange found that the state waited too long to formally update its enrollment projections and numbers with federal grant providers, resulting in the misallocation of $28.4 million.

The inspector general for the U.S. Department of Health and Human Services recommended Friday that Maryland repay that money and properly apply for reimbursement, which could be 50 to 90 percent of the original amount. The exchange’s executive director, Carolyn A. Quattrocki, said doing so would simply be an accounting exercise, although one that could result in the state owing the government about $5 million.

The Centers for Medicare and Medicaid Services, which oversees the funding of state exchanges, will ultimately decide what Maryland should do. Meaghan Smith, a spokeswoman for HHS, would not comment on Quattrocki’s $5 million estimation and said that federal health officials are reviewing the report.

More than a year ago, the HHS inspector general launched an investigation into Maryland’s exchange at the request of Rep. Andy Harris, Maryland’s lone Republican in Congress.

The exchange crashed on opening day in October 2013 and barely worked for months, making it difficult for many Marylanders to sign up for insurance made possible by the Affordable Care Act. The state has since spent tens of millions of dollars gutting and rebuilding the system and recently ended a much more successful enrollment period.

The malfunctioning site became a political liability for then-Gov. Martin O’Malley (D) and his second-in-command, Anthony G. Brown, who pledged to deliver the country’s best-performing ­exchange. O’Malley is weighing a presidential run in 2016, and Brown ran for governor last year but lost to Larry Hogan, a Republican businessman who frequently brought up the health exchange’s problems on the campaign trail.

Hogan and his staff are reviewing the inspector general’s report and have yet to make any decisions, spokesman Doug Mayer said in a statement, which referred to the original exchange as “a disaster which cost taxpayers millions.”

Several years ago, as the country began to implement the Affordable Care Act, Maryland officials decided to build a Web site through which residents could shop for private health insurance plans or sign up for Medicaid without having to use the federal site, HealthCare.gov.

To cover nearly all of the project’s costs, the state used $182 million in federal grants that paid for 100 percent of costs related to private plan sign-ups and 50 to 90 percent of costs related to Medicaid enrollments. (For any system-development costs, which were the bulk of exchange expenses, Medicaid covered 90 percent, according to an exchange spokesman.)

Maryland officials came up with a formula to determine how to split costs between the private plan sign-ups and Medicaid enrollments, based on who they expected to use the site most. Originally, Maryland predicted that 58 percent of enrollees would opt for a private plan while 42 percent would enroll in Medicaid, so that’s how costs were apportioned.

Early on, Maryland saw far more people enroll in Medicaid than in private plans. In February 2014, state officials announced that their original enrollment estimate was based on misinterpreted research, and they dramatically reduced the number of people they expected to enroll in private plans.

The auditors note that this was an opportunity for Maryland to change its cost-sharing formula — shifting more expenses to Medicaid, which requires the state to kick in some funding — but that it did not do so.

When the first enrollment period ended last year on March 31, 79 percent of enrollments were in Medicaid, compared with 21 percent in private plans. That was another opportunity to immediately update the formula, the auditors wrote.

The state updated its formula in June as it sought to repurpose some grant money to pay for fixing the exchange. Another update came in November, when the state sought permission to spend a final burst of grant money, according to the report.

Quattrocki, the exchange leader, said that the state is required to update its formula annually or when seeking more funding. The first enrollment period was a new, unknown experience, she said, so the state relied heavily on evolving instructions from federal officials. Plus, enrollment numbers were constantly changing — although publicly reported on the exchange’s Web site each month.

“It was all very fluid,” Quattrocki said. “The enrollment was ongoing.”

Andrew M. Slavitt, the acting administrator for the Centers for Medicare and Medicaid Services, wrote in a March 17 letter to the HHS inspector general that Maryland waited until last June to update its formula “because of the time needed for­ . . . enrollment data to stabilize and be successfully verified.”

The inspector general’s report says that update should have happened much earlier. In addition to revising the formula annually or when seeking grants, auditors wrote, states should also “promptly” revise the formula as soon as they receive “updated or better data reflecting a substantive change in program participation.” For example: On March 31 last year, Maryland’s tentative enrollment numbers showed a 37 percentage-point difference from original estimates.

“In our view­ . . . ” the report says, “the State agency should have used these enrollment figures to update the cost allocation methodology.”

The report also states that Maryland’s exchange lacked proper leadership in overseeing the use of the federal grant money, as it did not hire a chief financial officer until January 2014, months after the exchange launched.

Maryland has already made changes, Quattrocki said, such as updating its internal policies and practices. During the latest open enrollment period, which ran from Nov. 15 to Feb. 28, the number of private health plan enrollments increased dramatically, but Medicaid enrollments still made up nearly 58 percent of business on the exchange.