Beset by scandal over irregularities in test scores, Atlanta Public Schools has another, longer-running scandal on its hands: The district has underfunded its pension for custodians, bus drivers and cooks by more than a half-billion dollars.

APS has the worst underfunding of any large public pension plan in the state, according to a recent state audit. While it is generally agreed that, at any given time, a pension plan should contain 80 percent to 90 percent of the money it is obligated to pay out, APS has assets to cover just 17.4 percent of its pension promises.

The Jan. 1 report by the state Audits and Accounts Department found that pensions run by Georgia’s cities, counties and other local governments are under water by almost $4.5 billion. Three plans run by the city of Atlanta, plus the APS plan, accounted for nearly 40 percent of the deficit statewide.

The Atlanta Board of Education retirement plan, deeply in the red for decades, is now running a deficit of $532.5 million, according to the state. Last year, the school system deposited $46 million into the fund to help cover payments to the district’s more than 2,300 retirees. It will contribute another $39 million this year — roughly equivalent to the salaries of 557 teachers, said Chuck Burbridge, the district’s chief financial officer.

“It’s something that dates from long ago,” he said, but because past school boards didn’t adequately fund the plan, the district must put in large sums now to finance past promises.

The required contributions will rise in coming years, said Burbridge. “These are the cards we are dealt with,” he said.

Short of bankruptcy, employers are legally required to honor pension obligations. Some government units such as states can’t file bankruptcy.

The APS pension fund covers 2,362 retirees and beneficiaries and 974 active employees, mostly support staff who contribute up to 8 percent of their pay to the fund. The average pension was $24,170 in 2009.

Most teachers are in a separate state-run plan that is much better-funded. They contribute 5.53 percent of their pay for an average pension, in 2010, of $35,604.

Pension plans are underfunded when the long-term value of current and future pension benefits exceeds the plans’ assets. The problem has dramatically worsened nationwide in the wake of the recent financial crisis and recession.

Statewide, the average funding level of Georgia’s local government pension plans has continuously dropped since 2005, when it was 81.6 percent, to 69.2 percent in the most recent report.

The 272 city plans had the lowest average funding level, 61.5 percent. They were underfunded by $2.4 billion, but Atlanta’s city and school plans accounted for three-fourths of the cities’ total deficit.

State agencies are supposed to cut off any state payments to local governments that don’t meet the pension rules, but such sanctions sometimes don’t have much effect.

“If the state is not making grants to particular counties or cities, that is sort of a hollow threat,” said State Auditor Russell Hinton.