Officials of D.C. General Hospital, the city's only publicly financed hospital, have voted to close the facility July 1 if they cannot get $10 million more in operating funds for the current fiscal year.

Gilbert Hahn Jr., chairman of the D.C. General Hospital Commission, said a projected $10 million deficit for the current fiscal year, which ends Sept. 30, prompted the Tuesday vote. The city has budgeted $35 million for the hospital this year, Hahn said, but costs are expected to total about $45 million.

"The city budget office wanted to know what we could do if we had $10 million less to work with," Hahn said. "The answer hoped for was that we could cut here and cut there and still do a good job. But if we cut $10 million, we won't be able to operate," he said. Negotiations with the city are continuing and Hahn said he is "hopeful and optimistic" that the hospital eventually will get the additional funds.

City budget director Gladys Mack said last night that it is "unlikely" that the hospital will receive the full $10 million, but said "we're still in discussions with the hospital and trying to determine a way to resolve their budget problems."

Hahn attributed the facility's financial problems to a low occupancy rate, cutbacks in Medicaid and Medicare reimbursements and the hospital's use of staff doctors who do not bill patients directly.

In recent years, the hospital, which has an in-patient capacity of 1,000, has suffered from dwindling demands for its beds. Hahn said the average occupancy rate for the hospital now is 300 to 350.

Because of changes in the formulas for reimbursement, Hahn said the hospital expects the city and federal government payments for Medicaid and Medicare to be reduced about $4 million this year.

D.C. General receives more patients who qualify for free medical assistance than any other hospital in the District, Hahn said.

If the hospital's doctors operated under a "group practice" set-up, Hahn said, the facility would not have to bear the expense of the doctors' salaries because the doctors would bill the patients directly for their services.

Although Hahn described the hospital's financial status as "almost profitable" until this year, he said a $15 million to $25 million deficit is projected for the facility in fiscal year 1984, which begins Oct. 1.