The Prince George's County government has agreed for the first time to play a role in solving fiscal problems at Community Hospital and Health Care Systems Inc. by paying the hospital corporation $2.7 million for the right to collect about $11 million in years-old unpaid patient bills.

The county would keep the receipts from old debt it successfully collects and apply that money toward repayment of what is in effect a $2.7 million cash advance, county and hospital officials said yesterday.

County Attorney Thomas Smith said that the new plan will benefit both the county and the hospital corporation, which runs Prince George's General Hospital, the Bowie Health Center and the Laurel-Beltsville Hospital.

"There is no question in my mind that we will make over a half-million a year in collections ," Smith said. "Debt collection is systematic. If the debtor has it the money , we will get paid."

Smith said the county collected on all of the hospital's debts prior to 1983 when, in a move that was criticized in some quarters, the nonprofit corporation assumed management of the three hospitals. The county was bringing in about $1 million a year in payments, Smith said.

Robert J. Brady, president of CHHCS, said the county government is essentially resuming that responsibility.

"Assuming the county collects only 20 to 30 cents on the dollar of the $11 million , they will be whole," Brady said of the $2.7 million payment. "And if they do better, there will be a surplus."

Arnold I. Katz, a spokesman for Hospital Corporation of America Inc., a management firm recently hired to run the hospital, said the agreement is a "win-win situation."

"We are very confident that they will certainly more than recover the funds they have advanced to the system," Katz said.

In an interview earlier this month, Katz said the corporation had about $25 million in unpaid patient bills, excluding bad debts and other costs. The agreement would reduce that burden by nearly half.

HCA will still collect on bills incurred after 1983, and hopes to reduce the amount of time it takes to collect on those bills that remain on the hospital books from 120 days to about 65 days, Katz said.

Nearly $2 million could also be added to the hospital's coffers if the state reimburses the system for Medicaid expenses, Katz said.

In a related matter, former Bowie Health Center administrator Dennis L. McDonnell filed an $11 million suit yesterday in Prince George's County Circuit Court against the hospital corporation and HCA, charging that he was "wrongfully discharged" when former CHHCS board chairman Francis J. Aluisi fired him on July 17.

McDowell, who had been at Bowie for eight years, said in the suit that he was fired because he cooperated with government authorities in their investigations of wrongdoings involving the hospital corporation board.