A District of Columbia affiliate of the National Taxpayers Union is mounting a petition drive for a November referendum that would authorize an educational tax credit of up to $1,200 per pupil from D.C. income taxes.

The proposal is part of a nationwide push for tax credits or voucher payments aimed primarily at covering tuition costs for students to attend private schools. But the plan being offered to Washington voters would allow the money to be spent for supplemental programs at public schools as well as for private school fees. It would permit nonparents and even corporations to contribute their tax credits toward educating low-income youngsters.

Even though the petition forms were just approved last week by the D.C. Board of Elections, the plan already has drawn criticism.

"It's a crazy proposal," said D.C. school board president Eugene G. Kinlow. "I don't think it will ever come close to winning. If it did, the potential loss of revenue to the city would be so great that we would have to reduce services somewhere, and we're already hurting . . . It would be th death knell for public education, and it would be the death knell for educational equity. The people with clout and the ones who can negotiate the system might use it to get a better environment for their kids. The most vulnerble people in our society would be left behind."

But Jo Ann Willis, director of the D.C. Committee for Improved Education, which has launched the petition drive, said the main aim of the effort is to give parents of all income levels more choice in where to send their children to school.

"The kids who already are in private schools are not the ones we're worried about," said Willis, who lives in Alexandria and is not married. "The intent of the initiative is to give the same choice that wealthy people have already to the middle-income and poor people who are financially strapped to the public schools.

"Look, there's a great need for this in the District of Columbia," Willis continued. "Half of the first to third graders (in D.C. public schools) couldn't pass the tests to be promoted to the next level last month. It's an outrage what's happening in the schools here, and so many people feel helpless and trapped."

To get the referendum on the Nov. 3 ballot, about 13,000 signatures of registered voters must be collected by late June. Willis said her group is seeking 25,000 names, because past referendum drives have shown that manyof the collected names will turn out to be invalid. If the petition drive succeeds, the measure will be voted on at the same time as five seats on the D.C. board, including those of two of its most controversial members, Frank Shaffer-Corona and R. Calvin Lockridge, whose terms expire this year.

"We're offering sort of an alternative," said Jule Herbert, an official of the Taxpayers Union, "that people who are dissatisfied with the school board and the D.C. public schools might support."

Two referendum proposals -- one to legalize city-run daily numbers games and lotteries and another to make the District a state -- were approved by city voters last November.

Under the new proposal, taxpayers would be eligible for a credit, reducing their D.C. income tax by up to $1,200 per pupil, for all the educational expenses they pay for D.C. children in kindergarten "public or private schools which maintain racially nondiscriminatory policies." The credit would be less for families earning below about $20,000 a year, the level at which $1,200 in taxes is due. But non-parents who contributed to these children's education could get the same credit as long as the total spent per child did not exceed $1,200.

Willis said she expects many of the tax credit contributions to come from relatives and friends, but that fund-raising efforts also probably would be made by schools, neighborhood groups, churches and charities to attract money from childless strangers. Corporations could get tax credits for educational contributions for up to 50 percent of their income tax bill.

"People would pool their resources to help each other out at no cost," she explained. "No cost to them, but only to the D.C. treasury."

Willis said her group had not yet estimated how much the tax credit might cost the D.C. government, which collected about $340 million in income taxes last year. However, about 20,000 D.C. children already attend private school, and if the full credit was taken for each of them, the loss in tax revenues would be about $24 million. This year the city is spending $245.8 million on the public school system which has an enrollment of 99,225.

Tuition at private schools in the District now ranges from about $600 a year at Catholic parochial schools to about $4,000 a year at such private schools as St. Alban's and Sidwell Friends. Despite the expense, many private schools have far more applicants than they can accommodate.

The tax credits will encourage more private schools to be formed, Willis said, but she added: "I don't expect the public schools are just going to roll over and die." She said some parents probably will use their tax credits to buy extra equipment or hire extra teachers to upgrade their children's public schools.

"I believe the quality of D.C. public schools will improve," Willis said. "People are going to be able to do something about them. There'll be more competition, and quality is bound to rise."

Herbert, of the Taxpayers Union, said a petition drive for a similiar proposal collected about 400,000 signatures in California last year, but fell 200,000 short of the number needed to get on the ballot. A variant of the plan was offered by Ed Clark, last fall's Libertarian Party candidate for president. Herbert and several other initiators of the D.C. petition effort worked for Clark's campaign.

Bills for a simple private school tuition tax credit on federal income taxes have been introduced in Congress by Sens. Bob Packwood (R-Ore.) and Daniel P. Moynihan (D-N.Y.) and have won support from President Reagan. They have been bitterly assailed by a wide array of liberal, labor and public school groups.

One of the strongest critics, Albert Shanker, president of the American Federation of Teachers, has said the tax credits probably would be declared unconstitutional by the U.S. Supreme Court if they support religious instruction, and, in any case might well foster the creation of private schools by "extremist groups . . . (or) ethnic enclaves, rather than to bring children into the mainstream of American life."

The competition between public and private schools will be "inherently unfair," Shanker declared, as long as public schools are subject to laws and regulations on discipline, busing and handicapped children, and non-public schools are exempt.

"Our public schools can and must be better than they are in many instances," Shanker said, "but better or not, they must be preserved. For they were designed to keep our society together, . . . (not) pull it apart."