The federal government has a bad habit of paying some of its bills twice, according to the General Accounting Office, which examined the payment systems at three agencies and discovered more than $11 million worth of duplicate payments to various contractors and vendors.

The GAO, which has released three reports based on payment and refund studies at the three agencies, said the largest payment error involved $6.8 million that "was inadvertently disbursed twice" to a contractor for the Defense Logistics Agency.

The contractor discovered the error and refunded the money after about two weeks, according to GAO.

In its reports, GAO concluded that duplicate payments resulted from poor internal controls on payment transactions, including too much reliance on manual rather than automated payment files and procedures and a failure to record many of the payments promptly. Also, the GAO said, payment clerks did not always have full access to automated payment authorization records.

GAO surveyed payment procedures and transactions at the General Services Administration's national capital region finance center and the Justice Department's justice management division here, and the defense contract administration services region in Cleveland. It selected these federal payment centers for study because they process large numbers of invoices.

The review of payment records, conducted earlier this year, varied from agency to agency but focused on transactions that occurred during fiscal 1984 or early fiscal 1985.

GAO said most of the duplicate payments later were discovered by either the agency or the vendor and the money refunded. But given the problems found in the payment systems it studied, the agency said additional duplicate payments other than those it identified likely were made.

GAO conducted its studies at the request of Rep. Jack Brooks (D-Tex.), chairman of the House Government Operations subcommittee on legislation and national security.

Interest in the problem of duplicate payments grew out of news accounts in The Washington Post last summer about a Chevy Chase carpet firm owner who estimated she had refunded more than $300,000 in duplicate payments from the federal government during the past 20 years.

In July of last year, Joan Estrada, owner of Professional Carpet Service, copied 21 recent refund checks totaling more than $25,000 and mailed them to David Stockman, then director of the Office of Management and Budget. She said they represented her company's refunds of duplicate payments by 16 different agencies.

Estrada said the overpayments had gone unnoticed by the agencies and would probably have never been discovered if she had not returned the money.

At the time of last summer's disclosures about duplicate payments, several agencies complained that some vendors -- impatient when the government did not pay its bills on time -- contributed to the problem by sending out second bills that often got paid along with the first ones.

But GAO, while acknowledging that double billing puts a strain on the system, said the agency payment centers are supposed to be set up to prevent such mix-ups.

At the Justice Management Division, for instance, where $1.7 million in duplicate payment refunds were identified, GAO specifically looked at 17 duplicate payments to the Chevy Chase carpet firm. It said that "annotations" on 14 of the second billings "should have alerted payment center staff that a bill for the same services had been sent to them previously."

At the Defense Logistics Agency, GAO found 26 duplicate payments totaling $8.5 million, including the $6.8 million refunded by one contractor. At GSA, 32 duplicate payments totaling about $1.3 million had been erroneously authorized, GAO found.

GAO said that the agencies it surveyed already had begun making some improvements in their payment and accounting systems and would be making others based on recommendations in its reports.