The federal government has proposed creating a public corporation to run St. Elizabeths Hospital -- under joint federal-District control -- rather than turn the mental institution over to the District of Columbia government.

President Carter proposed the new administrative structure for the sprawling Southeast Washington mental facility as part of the fiscal 1981 federal budget plan that he sent to Congress yesterday.

For the District government, the president proposed a federal payment of $301 million and endorsed establishing a formula under which the figure would be set every year at 31 percent of local tax revenues.

Both the plan to transfer control of St. Elizabeths and the federal payment formula must be approved by Congress.

The federal payment is now limited to $300 million, although the president sought -- and failed to get -- a payment of $317 million for the fiscal 1980 budget. Congress ultimately appropriated $238 million toward a total city operating budget of $1.4 billion.

The payment is designed to make up for the tax dollars the city cannot collect for federal property and for unusual expenses the city incurs as the nation's capital. Its size is a bread-and-butter issue for local taxpayers. In general, the lower the payment, the higher the taxes residents must pay to maintain municipal services.

For the financially hard-pressed city, the long-standing proposal to transfer St. Elizabeths from the Department of Health, Education and Welfare to the D.C. government threatened to add to taxpayer burdens.

Congress appropriated $89.3 million in federal funds to run St. Elizabeths during the current fiscal year, and the president asked for $96 million for next year. This is an addition to $24 million that will be collected in fees from patients and the Medicare program.

Without a continuing federal subsidy, the transfer of the hospital the District's budget would saddle D.C. taxpayers with the total hospital expense.

HEW Secretary Patricia Harris said at a briefing on the president's budget that the plan to create a government corporation grew out of discussions with city officials, including Mayor Marion Barry, over the proposed transfer.

Under the White House proposal, the corporation would be accountable both to the secretary of HEW's soon-to-be-created successor, the Department of Health and Human Services and the mayor of the District. The corporation would use funds from both sources, but the split has not been determined.

One federal official said details of the transfer have not been worked out and it could take six to eight months to do so. Harris and Barry are scheduled to discuss the situation next month.

If HEW were simply to give St. Elizabeths to the District, Harris said, city officials could rightly respond that "it is an honor and a benefit we do not deserve."

St. Elizabeths, established in 1855 as a pioneering mental facility serving patients from all parts of the country, has evolved in recent years into a hospital that primarily serves the poor of Washington and beneficiaries of the federal government.

In the process, the once-model institution became a governmental step-child, declining to the point that in 1975 it lost its professional accreditation.

After Joseph Califano became Carter's first HEW secretary in 1977, he pledged to resurrect the hospital. At his urging, Congress pumped $52 million into the hospital's sagging physical plant and last August, it regained its accreditation.

Carter's proposal for adopting a formula to set the amount of the city's annual federal payment fell short of what city officials are seeking.

Under Carter's formula, the federal government would give the District 31 percent of the amount the city raises in local taxes -- or a projected $301 million for fiscal 1981, and an estimated $320 million in fiscal 1982. City officials want a formula based on 45 percent, which would raise $365 million. Whatever formula is adopted must be approved by Congress, where some key lawmakers have voiced objections.

In addition to the federal payment to the city's general fund, Carter requested $104 million as the first two years' federal contribution to a new pension fund for District police, firefighters, teachers and judges. Under legislation approved last year, the U.S. ultimately will pay $1.3 billion into the pension fund.

The proposed budget would end the District's abiltiy to borrow money from the U.S. Treasury to meet short-term operating expenses when its own bank accounts run low. After Oct. 1, the city will have to borrow the money commercially.

The president proposed an outlay of nearly $134 million next year for Howard University, an increase of $12 million over this year. Of the increase, $5 million would go toward improvements needed to assure the accreditation of university libraries, and the communcations, pharmacy and dental academic programs.

For Gallaudet College for the deaf, the president proposed spending $49.8 million, an increase of $1.5 million.

The budget also proposes $275 million in construction funds for the Metro subway system, a figure equal to the cost of several never-constructed interstate highway projects in this area that have now been stricken from the budget. An additional $69.5 million would go to Metro for a subsidy on the repayment of construction bonds.