Treasury officials said that everything had been done legally. But they confirmed in a recent interview that the correct amount for that year’s pension contribution was zero, which appeared in an actuarial report. They explained that the conflicting figures elsewhere had been inflated by other items, like health care contributions.

If New Jersey violated federal securities, tax or other rules, it could be forced to make up some of the contributions. The Internal Revenue Service has very specific rules against mixing pension money with money for other uses, like health care. Federal securities law also requires bond issuers to provide complete and accurate financial information.

The New Jersey Education Association has sued the state for failing to put enough money into the teachers’ pension fund. The lawsuit does not describe all the accounting maneuvers, but a State Superior Court judge has held that the case, now scheduled for trial in May, can proceed.

State law requires New Jersey’s seven pension plans, large and small, for various types of public employees, to be funded according to actuarial standards. Over the last decade, though, the Legislature has passed, and various governors have signed, a series of amendments to statutes that allow smaller contributions or none. These were justified by various maneuvers and approved with little scrutiny. In interviews, officials of the Treasury said the changes were made at the behest of the Legislature, while legislators faulted the Treasury.

Donald T. DiFrancesco, the acting governor in 2001, when the Legislature approved an expensive pension increase for teachers and other state employees, said he recalled that “people thought it was good public policy,” devised to attract the best people. He said he did not think the measure was considered financially unsound and did not recall anyone challenging it or calling it improper.

The state’s practices have nevertheless left its retirement system in a much more perilous condition than is widely understood.

“If people ran their households like this, they’d be in bankruptcy,” said Lynn E. Turner, a former chief accountant for the Securities and Exchange Commission. “If businesses did, the best example is the old steel mills when they got so far behind and didn’t fund their pensions as they should have. It tipped them into bankruptcy.”