Eight days after the Supreme Court upheld a Minnesota law allowing parents of children in public or private schools a tuition tax deduction of up to $700, New Jersey state legislators introduced two bills to permit a tax deduction of up to $1,000 for children's school expenses.

In Wisconsin, two legislators recently told Charles M. Phillips, executive director of the Wisconsin Catholic Conference, that they would draft a tuition tax deduction bill "just to see what the fiscal note giving the bill's cost would be," Phillips said. But unless a proposed change in the state constitution succeeds, such a measure is likely to run into an impassable constitutional barrier.

So far, those cases apparently represent the only state reaction to the court's June 29 ruling, despite opponents' fears that it could trigger similar laws that would divert badly-needed tax revenue away from public schools.

In state after state with high enrollment in parochial and other private schools, educators, state officials and lobbyists said little or no effort has been made to mimic Minnesota. With many legislatures not now in session, further action seems unlikely before fall or winter, if then.

The reasons vary, but two factors are cited repeatedly.

First, economic times are hard. State taxes are going up while services are being trimmed, particularly in many of the northeastern and midwestern industrial states--normally the most fertile ground for tuition tax benefits. The recession is particularly pressing urban areas such as Chicago, New York, Philadelphia, Milwaukee and northern New Jersey, where blue-collar ethnic groups with a Roman Catholic heritage are an important part of the political fabric and parochial school enrollments are high.

"This kind of legislation puts a hole in the purses of these states," said Thomas A. Shannon, executive director of the National School Boards Association and a staunch opponent of tuition tax credits. "These bills may be constitutional now, but what is constitutional is not necessarily what is wise."

Second, lobbyists for Catholic groups in many of those areas, who are among the most persistent supporters of tuition tax benefits, say that they prefer to push Congress to pass the Reagan administration's federal tuition tax credit legislation rather than divide their attention among the states.

"What we have felt," said Father John Quinn, executive director of the Illinois Catholic Conference, "is that if you've got a bill like the federal one, it makes all the sense in the world to get behind it, get it passed and have it go to the courts for a decision rather than have different bills all over the country and a lot of confusion. It makes sense to concentrate your efforts."

The concept of tuition tax deductions or credits has been debated for nearly two decades and came closest to being enshrined in federal law in 1978, when Congress passed credit measures but failed to agree on who should benefit: parents of college students or those of elementary and high school students.

Both the Minnesota law and the federal credit legislation before Sen. Robert J. Dole's (R-Kan.) Finance Committee offer benefits to parents of elementary and secondary students. They make no provision for college tuition.

The federal measure would provide more benefits than the Minnesota law. The federal bill would offer taxpayers a direct credit for 50 percent of their tuition costs, up to a maximum of $100 per child in the first year, $200 the second and $300 thereafter, with more limited benefits available to those who earn over $40,000. No benefits would go to parents with incomes above $50,000.

Minnesota's law provides more indirect relief, allowing maximum deductions of $700 from the gross income figure on which taxes are calculated.

A 1982 study for the Institute for Research on Educational Finance and Governance showed that "about 88 percent of private school children are in church-affiliated schools . . . the eligible population under a tuition tax credit would be more involved in religious institutions than . . . the population at large."

Nationwide, about one child in nine--a total of 5 million--is enrolled in nonpublic schools. About 60 percent of children in private schools are enrolled in Catholic schools. Baptists, who claim the next largest enrollment in sectarian schools, teach about five percent of children in private schools.

The study's author, James S. Catterall, an assistant professor at UCLA, said that "a disproportionate number of families in the Northeast and North Central regions would benefit, but because of countervailing tuition patterns, total tuition tax credit dollar benefits would favor the South and West . . . where a relatively smaller number of parents would receive larger credits." He added that "tuition tax credit benefits would be concentrated in the central cities . . . ."

Even so, the political climate of the South and West is relatively less receptive to tuition tax benefits. The major exception in the South is Louisiana, where a strong Catholic presence has contributed to the state's position as the most generous supporter of private schools in the nation.

Among the support offered in Louisiana is a four-year-old tuition tax credit law offering $25 per child to parents of children in either public or private schools. Such other aid as the loan of textbooks and funds for teacher training cost the state nearly $200 per child, according to Emile Comar of the Louisiana Catholic Conference.

Several other states including New Jersey, Pennsylvania and New York--which each have one child in six enrolled in private school--also offer extensive support for private school students in the form of transportation, loaned textbooks and, in some cases, auxiliary services ranging from computer software to standardized tests to guidance counselors.

In Ohio, such aid costs $172 per student, for a total of $43 million. Pennsylvania, where a recently expanded sales tax has helped the state emerge from recurrent budget crises, offers an average of $137 in support of each private school student, for a total of about $47 million.

Yet such aid, which received Supreme Court sanction after laborious litigation, has been circumscribed recently by financial considerations. In the past three years, Illinois Gov. James R. Thompson, citing the state's bleak economic picture, has twice vetoed measures expanding transportation assistance for students in private school.

Other states, such as Michigan and California, have significant private school enrollments, but their constitutions bar aid to religious organizations. Connecticut has a higher-than-average private school enrollment but no state income tax.

A California group, Parents Choose Quality Education, is preparing a school voucher initiative for the November, 1984, ballot. The initiative, more generous than the federal tax credit proposal, would authorize the financially strapped state to provide vouchers worth about $1,850 per school-age child in 1983 terms, according to Roger Magyar, the group's co-founder.

"The state money would go to parents, and parents would decide where to use it," he said.