A federal audit published Tuesday said New Jersey claimed $300.5 million in unallowable costs to Medicaid for special-education services, plus an additional $306.5 million in reimbursements using payment rates based on costs that were not properly established.

The state incorporated into its rates more than $400 million in school employees' pension costs even though it has not made scheduled payments into the fund in nearly 20 years, the Office of Inspector General at the U.S. Department of Health & Human Services said.

Under federal law, schools must provide special-education and related services to children with disabilities, but Medicaid covers only a portion of  the evaluations used to determine whether children are eligible for special-education benefits. New Jersey, relying on rates developed by a contractor, Public Consulting Group, claimed reimbursement for ineligible expenses, the audit said.

The report by the inspector general covered services from July 2003 through June 2015. It said New Jersey should pay back $300.5 million and work with the Centers for Medicare and Medicaid Services to determine how much of the $306.5 million it should pay back.

The New Jersey Department of Human Services said the auditors were wrong and noted that the report is just the first step in a process that can be appealed within the federal Health and Human Services Department, and then in federal court, if needed.