Government aid to private schools already is substantial in many parts of the country, including the District of Columbia -- even without the education tax credit on Washington's Nov. 3 ballot.

"The issue isn't whether or not to aid private schools," said Dennis J. Encarnation, a researcher at Stanford University. "They're already getting considerable aid. The issue is how much to increase it."

If adopted, the $1,200 credit here would be the most generous private school aid program in the country. But Washington is just one of many battlefields -- including state legislatures and the U.S. Congress -- where private-school backers and anti-big government conservatives have tangled with public-school supporters.

Those who want private school aid have made substantial gains. In Louisiana, private-school students have received free textbooks from the state since Huey Long was governor 50 years ago. Private-school youngsters get free texts in 15 other states, too. In almost 30 states they get free bus rides to school. Throughout the country, private schools take part in 46 federal education programs.

In Washington, private schools get considerable aid: reduced-price bus tokens and subway farecards, federally subsidized lunches and aid for about 1,000 low-income students and 468 who are handicapped and attend nonpublic schools.

As in virtually all states, the property of nonprofit schools is tax-exempt in the District. Gifts to the schools qualify as charitable contributions that can be deducted from gross income, reducing the D.C. and federal taxes their donors must pay.

n a paper prepared for the National Institute of Education, Stanford researcher Encarnation estimated that about one-quarter of all funds for private schools in the United States now comes from public sources.

The aid has increased, he noted, despite a long string of U.S. Supreme Court decisions, barring some forms of it -- including several versions of state tuition tax credits.

"The courts knock down one thing, and the states come back with something else," Encarnation said at a conference on tuition tax credits sponsored in Washington last week by NIE and Stanford's Institute for Research on Educational Finance and Governance.

Over the past decade, as criticism of public schools has mounted, support for private-school aid has come not just from the private schools themselves, but from groups opposed to high taxes and "big government," such as the National Taxpayers Union.

The NTU is spearheading the initiative in Washington, after failing in 1979 and 1980 to collect enough signatures to get a similar measure on the ballot in California.

The recent aid proposals have taken two principal forms -- tax credits that would reduce taxes by the amount individuals spend on schools, and vouchers that would provide public money for parents to spend at the schools of their choice.

Both notions have attracted support from prominent scholars, including conservative economists Milton Friedman and Thomas Sowell and sociologists James S. Coleman and Christopher Jencks.

They have drawn considerable scholarly opposition as well along with heated attacks from teachers' unions and other public-school groups, including the PTAs and virtually all groups of school administrators. The same broad array, along with civil rights groups and the American Civil Liberties Union, is fighting the tax-credit proposal in Washington.

None of the prominent academic supporters of tax credits or vouchers has specifically endorsed the D.C. tax-credit proposal, which would allow a reduction from local income taxes of up to $1,200 per student for expenses at either private or public schools.

But Friedman, a Nobel Prize-winner now at Stanford, strongly endorsed the prototype of the D.C. initiative that the NTU promoted in California, and Sowell was honorary chairman of the group's unsuccessful California ballot drive.

In a statement distributed by NTU, Friedman praises the proposal, which permits tax-free donations for low-income children. "Its effects would be essentially identical with the kind of unrestricted educational voucher plan that I have been supporting and promoting for decades," Friedman said.

"Either plan would give all families, from the very poorest to the very wealthiest, the effective freedom to choose the schools their children attend, a freedom that is now available only to those families that can afford to pay twice for schooling," he said.

Coleman, whose massive research in the mid-1960s strongly favored desegregation, has supported federal tuition tax credits, which almost passed Congress in 1978. This year the credits have received support from President Reagan, but their chances in Congress are considered slim because of federal budget deficits.

On the other hand, David W. Breneman, a senior fellow at Brookings Institution, contended that the credits are an expensive and inefficient way to promote school choice because a great deal of the tax revenue lost by them would be kept by upper-income families who already have children in private schools.

The only new group that might be able to switch from public to private schools, Breneman said, are lower middle-income parents on the "margin of choice."

"I don't believe that tuition tax credits would gut the public schools," Breneman said at the tax-credit conference. "But the parents most concerned with the schools are the ones most likely to leave, and the quality of public schools would go down more than the numbers."

Over the past decade, tuition tax credits for private schools have been passed by state legislatures in New York and New Jersey, and struck down as unconstitutuional by the U.S. Supreme Court.

In Minnesota, a less expensive deduction from taxable income for expenses at both private and public schools was upheld by a federal district court. But it is being challenged in the Court of Appeals, and a similar plan in Rhode Island was struck down by a federal judge.

A credit of $25 per student was passed by the Louisiana legislature in 1979, and so far has not come under legal challenge.

According to Donald Jensen, a Stanford researcher who attended the NIE tax credit conference, the Supreme Court has used a three-part test to invalidate tax credits under the First Amendment to the U.S. Constitution, which bars the "establishment of religion."

The law must have a secular purpose, he said, and have a primary effect that neither advances nor inhibits religion. It also must not foster "an excessive government entanglement with religion."

Under this reasoning, Jensen said, tax-credit plans will almost certainly be ruled unconstitutional.

However, Jensen noted that the high court has upheld substantial aid to parochial and other private schools on the theory that it was primarily a "child benefit" and has also approved federal aid to church-related colleges.