D.C. General Hospital, facing a deficit expected to reach $10.5 million by Sept. 30, 1984, asked the mayor and City Council yesterday for a $4.2 million subsidy and a package of administrative changes that would give the hospital greater autonomy and make up the balance of the $10.5 million.

In a report submitted to city officials, the hospital's governing commission said it already had benefited from a series of plans and actions that reduced the prospective deficit from a $31 million figure envisioned in January.

Last December, the commission that oversees D.C. General voted to close the city's only publicly financed hospital July 1 if it could not meet its projected deficit for the current fiscal year.

An agreement with the mayor in January providing at least $4 million more for the hospital in the current fiscal year staved off that threat, but did not make up the full deficit.

In commenting on the report sent to the mayor and council yesterday, Gilbert Hahn Jr., chairman of the D.C. General Hospital Commission, appeared encouraged about the future of the hospital.

While the report "by no means entirely solves the problem," he said, "it represents placing us in an entirely different position than we were in six months ago."

He said that a series of proposals outlined in the report that would give greater autonomy to the hospital would save money and improve services.

There "isn't any question," said Hahn, a Washington lawyer and former City Council chairman, that an experiment in gaining greater autonomy for the hospital, begun four years ago, "has been very successful."

The five proposals, which the report said would save a total of $6.4 million in the year starting Oct. 1, include immediate establishment of a separate bank account for the hospital and exemption of the hospital from residence requirements of the D.C. Comprehensive Merit Personnel Act. Hahn said the separate bank account would enable the hospital to earn interest and to get discounts through faster bill payment.

The hospital is also asking for exemption from the reimbursement limit in the D.C. Medicaid program and for a continuation of another Medicaid payment arrangement that was established for this year.

In addition, the hospital commission asked for construction contracting authority, which it said would cut costs and boost efficiency.

Besides Mayor Marion Barry's agreement to increase the hospital's subsidy $4 million this year and $8 million next year, the report said the deficit has already been cut by measures that include a two-year reduction of $5.2 million in the hospital budget, a three-year, $2.3 million contract to provide services at D.C. General and by a Medicaid reimbursement agreement negotiated for this year.