The federal tax cut that President Reagan signed into law yesterday will bring automatic state tax cuts amounting to tens of billions of dollars over the next five years. These will sharply reduce revenues in Maryland and Virginia, according to calculations by state officials and independent tax groups.

The District of Columbia also is expected to lose revenue, but the probable impact will be less than on the states, city officials said.

Most of the non-federal cuts will be in business taxes.

Many state tax codes are linked to the federal internal revenue code, so that state revenues automatically fall as federal tax rules are liberalized. The National Governors' Conference has projected such linkage will cost states a total of $2.3 billion in the 1982 fiscal year. This figure is likely to shoot up powerfully in subsequent years as more generous federal depreciation allowances for business take full effect.

Maryland, Virginia and the District of Columbia stand to lose more than $26 million in 1982 and more than $900 million over six years just because of the depreciation speed-up in the new federal law. Additional revenue losses are likely in Maryland and Virginia because their personal income tax collections are also linked to the federal code.

The theory underlying the Reagan administration's tax bill is that it will stimulate investment and economic growth. Supporters say the tax cuts will thus eventually increase rather than diminish federal revenues, and by extrapolation would also enrich state governments. Officials in Virginia say they believe that will happen, but other states are focusing more on the probability of short-term revenue loss than on the possibility of long-term gain.

State and local governments are already struggling to compensate for reductions in federal aid under the budget cuts that Reagan also signed into law yesterday. A simultaneous loss in tax revenues would almost certainly force many states to choose between raising tax rates or reducing services.

"It's conceivable that the impact could be very major," said Robert Rader, Maryland director of revenue estimates, though he said he was "still trying to develop ball park figures" for the total impact on Maryland.

The accelerated depreciation formula, which allows businesses to write off the cost of new plant and equipment faster than they can now, will have an almost immediate impact, he said, but personal income tax changes will not begin to be felt until 1983, when tax returns covering income earned in 1982 are filed. A reduction in personal income taxes paid to the state would also affect Montgomery and Prince George's counties, where taxpayers give the county governments a flat 50 percent of whatever they pay the state.

State finance officers across the country have been scrambling to figure out the new law's impact on their revenues. The impact will vary because some states key their personal and business income taxes to federal formulas and some do not, and some states have no personal income tax.

Citizens for Tax Justice, a research organization sponsored by labor unions and public-interest groups, said the states could lose $27.5 billion over the next six years from the new depreciation formula alone and the annual cost to the states could reach $10.2 billion by 1986.

In Virginia, however, state tax officials have concluded that the tax-cut bill will stimulate overall improvement in the economy, just as administration officials promised, to the extent that the state will actually come out ahead as sales and income tax revenues go up.

Nancy Beitzel, senior research economist in the state tax division, said Virginia expects to lose $16.5 million in corporate tax revenue in 1982, $35.1 million in 1983, and $55.9 million in 1984. In addition, she said, the state will lose $7.5 million in estate tax revenues in that time, because its estate tax is keyed to the federal estate tax, which the new law virtually eliminates.

But, she said, "as a result of the improved economic outlook, we believe the Virginia economy would perform better and we would collect more income and sales tax revenues. We believe that on net we will come out ahead on revenues."

She said state tax officials made a preliminary report to the state Senate calculating that sales and income tax revenue would go up by $45 million in 1982, by $91 million in 1983, and by $84 million in 1984, far outstripping the potential loss in corporate tax revenues.

D.C. finance director Carolyn Smith said the city, already strapped for cash, expects to lose $2.5 million in revenues in 1982 because of the new depreciation formula and more in subsequent years, but she said "the impact won't be so great on us because we are not heavily industrialized."

Personal income tax revenues in the city will not be much affected by the changes in the federal law because the District uses its own formulas for calculating taxable income and tax rates.

Maryland and Virginia, however, use adjusted gross income as calculated on federal tax returns as the basis for their state income taxes.

Rader said that any federal tax exclusion that reduced adjusted gross income, such as the new 15 percent net interest exclusion effective in 1985, would reduce state income taxes accordingly. But federal tax cuts that are in the form of deductions from adjusted gross income or credits against taxes owed would not necessarily impact on the states because they do not always follow the federal code in these respects.

Beitzel said Virginia officials had made a "preliminary analysis of the tax bill and we don't see a lot that would affect the adjusted gross income." The biggest potential problem for Virginia, she said, may be the elimination of the so-called marriage penalty, under which two workers pay more federal tax if married than they would if single. The penalty is reduced by not counting part of the income of the lower-paid spouse. "We don't know if it will be an exclusion, reducing adjusted gross income, or a deduction, where it won't reduce it," she said.

Maryland and the District have already eliminated the marriage penalty through the use of a combined tax return in which working spouses can file separately on one form.