President Reagan's proposed cuts in federal grant programs would wipe out projected budget surpluses in three-fourths of the states, leaving most of them with large deficits, according to studies released yesterday by the American Federation of Teachers and the National Association of State Budget Officers.

The studies used somewhat different methodologies but both came to the same conclusions. At present, budget deficits are projected for 1985 for the District, Vermont and Alaska, but the budget officers say all other states will either balance their operating budgets or have surpluses by the end of fiscal 1985, totalling $5.2 billion nationwide.

The budget officers estimate that if President Reagan's cuts in grants to the states are approved, they will total more than $9 billion in outlay cuts, and wipe out the surpluses in all but 14 states, throwing the rest into a deficit position. But since deficits are forbidden in virtually every state, the states will be required to either cut their services or raise taxes to end up in the black.

The AFT study, using federal budget authority reductions for fiscal 1986 instead of outlay reductions, estimated the cuts at closer to $20 billion. However, they also concluded that all but 14 states would lose their surpluses and face serious deficits.

Both studies agreed that Connecticut, Delaware, Hawaii, Kansas, Minnesota, Missouri, Nevada, New Hampshire, New Jersey, New Mexico, North Dakota, South Dakota and Wisconsin would continue to post a surplus despite the cuts. The budget officers concluded that California would post a surplus,w hile the AFT added Wyoming to its list.

All the rest would face deficits, ranging from small amounts to over $1 billion in New York.

A separate study of Medicaid prepared for the National Conference of State Legislatures found that from 1982 to 1984, the District lost $19.78 per person (based on total population) as a result of Medicaid funding cuts engineered by President Reagan in 1981.

The District's per capita loss was by far the highest in the nation; the national average was only $3.85 per capita and the figure for Virginia was $1.97 and for Maryland, $4.62.

The same study found that regionally, the Northeast was the biggest loser per capita, at $7.74, followed by New England at $6.81 and the Plains states at $5.18. By contrast, losses in the far western states were only 14 cents per capita over the three years and in the Southwest, only 22 cents.

The figures differ sharply from region to region because Medicaid grants to states vary according to the state's per capita income, the kinds of services its Medicaid program provides and the population groups it covers.

The study, conducted by Federal Funds Information for States, which is financed by the NCSL and the National Governors' Association, also projects that in fiscal 1986, not counting any special hardship funds that may be given out to cushion losses under the president's proposals, New York would be the biggest loser of total dollars for benefit payments under the president's new Medicaid proposals -- $470 million.