Maine families on food assistance won’t have to repay benefits that were erroneously handed out by the Maine Department of Health and Human Services, federal officials said this week.

DHHS in late July notified about a third of the Mainers who rely on the Supplemental Nutrition Assistance Program, commonly known as food stamps, that their benefits would be reduced to recoup the nearly $5 million in overpayments the state had made.

But the U.S. Department of Agriculture, which oversees and pays for the program, in a letter this week prohibited DHHS from collecting the overpayments from recipients and billed the state for the full amount, $4,861,920.

Between April and July 2011, the program paid about a third of the program’s beneficiaries, or 70,000 households, more than federal regulations allowed. The overpayments went out after the federal government decided to cut back the portion of benefits that helps recipients pay their utility bills. The USDA had previously temporarily boosted those benefits when oil prices rose to record levels last year, so the reduction was a readjustment.

Maine law prevented DHHS, which administers the program, from reducing benefits until a formal rule change in the program was made, according to the department. In June, DHHS restored benefits for a several-month period to comply with state requirements, according to the Sept. 24 letter from James Arena-DeRosa, northeast regional administrator for the USDA’s Food and Nutrition Service, to DHHS Commissioner Mary Mayhew.

“It is unfortunate that Maine did not pursue a consultation with FNS,” the letter states. “This would have afforded FNS the opportunity to properly advise the state of their legal responsibilities and options, and likely would have prevented the establishment of these claims.”

Affected households were overpaid by up to $20 for each month, according to the letter.

Congresswoman Chellie Pingree, D-Maine, said many families complained about having their benefits cut to make up for DHHS’ error.

“We heard from dozens of food stamp beneficiaries who suddenly, out of the blue, were informed that they owed the state $80,” she said in a statement issued Thursday. “For people struggling to put food on the table, that represents a big hit to their budget. These families didn’t do anything wrong; the overpayment was due to an administrative mistake, and there was no way they could have possibly known they were getting a few dollars more a month than they should have.”

The feds are asking Maine to pay back about $2.8 million of the $4.8 million that’s owed. USDA deducted from the total about $2 million in bonus awards that the state was eligible for in fiscal year 2011.

DHHS has 10 days to file an appeal of the claim.