Every weekday, 16-year-old Paula Roby rides a van from her home in St. Paul to Regina Catholic High School in neighboring Minneapolis, and the state of Minnesota picks up 40 percent of the fare.

Once at school, Paula and her classmates study with textbooks provided free of charge by the state. The cost of the students' guidance counseling and school health services is subsidized by the state. If Paula or any of her classmates want to take language, mathematics or science courses not offered at Regina, the state will pay to have them take those classes at a Minneapolis public high school.

And each spring, Paula's father John, a $30,000-a-year purchasing agent for the University of Minnesota, and her mother Lucille can deduct $700 of Paula's $1,400-a-year tuition from their taxable income before computing their state income taxes.

"It state aid has been crucial all through the years," said Lucille Roby, who sent all nine of her children to Catholic schools. "We pay for the public schools through property taxes , right? And in turn, they should help us."

State aid for families of nonpublic school children, a gripping issue in Washington's Nov. 3 election, has been a way of life in Minnesota since 1955, when the state legislature approved the first and only U.S. tax deduction for public and private education to have withstood a court test.

Minnesota's private schools have prospered, public schools have not been damaged, taxes have not skyrocketed -- in part because the state aid offered here is far less than the $1,200 per pupil credit proposed for Washington.

Minnesota is not the District of Columbia, though both public school systems are wrestling with tight budgets and declining enrollments. Here in Minnesota, the public school students regularly score higher than the national average on standardized tests. Minority enrollment is no higher than 31 percent in any school district and almost negligible in most.

By contrast, Washington's public school students usually score far below the national average and 95 percent of the city's public school students are black, nearly half of them coming from relatively poor families.

Still, Minnesota's quarter-century experience, which proponents of the $1,200-per-student D.C. tax credit studied in hopes of avoiding legal minefields in their own proposal, may offer the few concrete clues to the impact of state aid to nonpublic schools in the United States.

For instance:

The aid to private schools did not accelerate the decline in public school enrollments, officials of Minnesota public and private schools agree. Instead, it helped to stabilize enrollment in Minnesota's 540 private schools, which had declined by nearly 40 percent between the mid-1960s and mid-1970s. Most of those schools are Catholic.

"We continue to hear the bromide that tuition tax credits would destroy the public schools," said Msgr. James D. Habiger, executive director of the Minnesota Catholic Conference. "But the only track record for that in the country is here in Minnesota, and it didn't happen."

Most of the major aid programs, including a short-lived $100 tax credit for families with children in private schools, drew stiff legal challenges from the Minnesota Civil Liberties Union (MCLU), school boards, teachers' organizations and citizens groups dedicated to the separation of church and state.

A three-judge U.S. District Court panel upheld the constitutionality of Minnesota's $700 tax deduction in June 1978, in a case brought by the MCLU. However, the law was challenged again in 1979, and the case is now before the 8th U.S. Circuit Court of Appeals in St. Louis, with the outcome in doubt.

Having gone down the road of aid to nonpublic schools, the state legislature now may demand some say in how those schools are operated.

The Minnesota House Education Committee held hearings last week on a bill to set minimum standards for private schools and to require the licensing of nonpublic school teachers.

Supporters of the bill say it was designed primarily to rein in a rash of tiny "home schools" set up by fundamentalist Christians for their children. But the state's large, prestigious private preparatory schools view the bill as a threat to their independence and are vehemently opposed to it.

"If we have to be subject to any regulations . . . we'd just as soon not receive any support," said John Littleford, headmaster of the highly regarded, 880-pupil Breck School, located in Golden Valley, a suburb of Minneapolis.

Finally, Minnesota's package of state aids and tax breaks for nonpublic schools has not caused a major drain on the state's treasury, as some had feared. Nor has it resulted in a hefty increase in taxes. Expenditures constitute about 1 percent of the $1.3 billion the state spends annually on elementary and secondary education.

During the 1979-80 school year, for example, Minnesota spent $16.4 million in nonpublic school aid, according to the state Senate's research staff, including $2.2 million for the education tax deduction.

That works out to an average of $180 for each of the 90,954 students in Minnesota's private schools. However, the per-pupil expenditure, based on a formula, varies from one school district to another. In St. Paul, for example, every private school student is entitled to about $245 in state aid.

Aid to nonpublic schools was more costly between 1971 and 1973, before the Minnesota Supreme Court struck down a tax credit that was offered to parents of children in private schools.

Parents could subtract up to $100 of each child's private educational costs from the income tax they owed the state. Moreover, the credit was "refundable." That is, low-income families that owed nothing in state taxes were entitled to a refund from the state to cover up to $100 of their children's tuition and textbooks.

At least half the eligible parents claimed the credit during the three years, at a total cost to the state of $28 million, according to state Department of Revenue figures.

"It was a factor in helping to stabilize the enrollment in Catholic schools," said Msgr. Habiger, of the Minnesota Catholic Conference. "It helped in that period of dramatic change for us."

Catholic school enrollments declined nationally during the late 1960s and early 1970s, a time of great religious and social upheaval within the church. Parochial schools were hardest hit by rising transportation costs and skyrocketing payrolls for lay teachers, who were hired to replace priests and nuns who left the fold.

Minnesota aid to nonpublic education apparently enabled some financially strapped Catholic schools to stay afloat, while easing the burden of low- and moderate-income families that were facing mounting tuition bills.

Last year, 10.8 percent of Minnesota's 49,375 school-aged children attended private schools. Nearly 30 percent of St. Paul's children and 20 percent of Minneapolis' children are in private schools. (About 17 percent of Washington's students are in private schools.)

Tuition in the Twin Cities Catholic elementary and secondary schools ranges from $300 to $1,400 a year. Some parents spend as much as $5,000 a year to send their children to Breck, St. Paul Academy and other prestigious prep schools (the equivalents of schools like St. Albans in Washington, where tuition is $4,290 a year).

"I'm convinced a lot of those schools wouldn't have made it without that state help," said Larry Harris, coordinator of legislative and community relations for the Minneapolis public schools.

"I think there are a lot of families staying in nonpublic education because of it . . . But I don't think parents are making a conscious decision to go to the nonpublic schools because of the aid," he said.

Kenneth A. Berg, deputy superintendent of the St. Paul schools, acknowledged that aid to nonpublic schools "has not been detrimental to us," primarily because "the aid given to those schools now doesn't really solve their financial problems."

But a sharp increase in state aid might prompt families to transfer their children from public to private schools, in search of what they perceive as a better education, he said. Public schools would lose state funding as the size of their classrooms shrank.

Donald C. Hill, president of the 45,000-member Minnesota Education Association (MEA), the state's largest and most influential teacher's organization, said that increased state aid may prove to be a double-edged sword for private schools.

"It's only a question of time before private-sector teachers organize for collective bargaining purposes, which will cause the same problems including strikes that we've got in the public sector right now," he said.

State Sen. Gene Merriam, a Democrat from Coon Rapids, a rural community north of Minneapolis, and a leading advocate of nonpublic school aid, said it helped to "strike a degree of equity" for families with children in private schools who pay taxes for public schools.

Echoing that theme, Imogene Treichel, executive director of the Minnesota Citizens for Educational Freedom, said the state aids promoted pluralism and the parents' right to choose the kind of education they want for their children. Treichel has two children of her own and two foster children, who attend special education classes in a parochial school.

"When you say I'm a thief of the public treasury, I have trouble being receptive," said Treichel, whose group vigorously lobbied for passage of the private-school aid programs.

The turning point in that battle occurred in 1969, when the state legislature approved the transportation aid program. Two years later, the legislature enacted the $100 tuition tax credit. The tax credit was ruled constitutional by a state court judge in St. Paul in July 1972, but that decision was reversed by the Minnesota Supreme Court in November 1974.

The Minnesota legislature responded the following year by approving what amounted to a series of indirect credits, including funds for nonreligious textbooks, counseling and health services in the private schools.

Then, in 1976, the legislature increased the educational tax deduction from $200 to $500 for children in public or private elementary schools and to $700 for high school students.

A U.S. District Court panel upheld the constitutionality of the deduction in June 1978. However, the law was challenged again in 1979 in another suit. U.S. District Court Judge Robert Renner upheld the law for a second time in May 1981. However, Renner's decision has been appealed to the 8th U.S. Circuit Court of Appeals in St. Louis.

William I. Kampf, a St. Paul lawyer representing the plaintiffs in the case, said he was heartened by a November 1979 ruling in Rhode Island that struck down an educational tuition tax deduction, nearly identical to Minnesota's, on the grounds that it advanced religion.

The Minnesota deduction differs from the tax credit being proposed in the District of Columbia in the way it is computed, its potential fiscal impact and its scope.

Minnesotans can benefit from the deduction only if it moves them into a lower tax bracket or appreciably reduces their taxable income. In any event, the cost to the state has been slightly more than $2 million a year.

On the other hand, the proposed D.C. tax credit would permit parents to reduce their D.C. income tax obligation by the amount they spend on their children's education to a maximum of $1,200 for each pupil.

In Minnesota, taxpayers may only claim deductions for tuition, transportation and textbooks. However, in upholding the law, Judge Renner said it was open to a rather liberal interpretation.

For instance, he said, parents could deduct fees for their children's tutoring, summer school classes, or attending a public school outside their district. Driver's training courses are deductible if taught as part of the school's curriculum, he said.

Also, tennis shoes and sweat suits purchased for gym classes are deductible, as are school fees for ice skates, calculators, musical instruments and shop class materials.

The deduction and other Minnesota state aids have been most beneficial to families like the Robys who literally operate on the margins.

The Robys have managed to send nine children to Catholic schools and maintain a comfortable, three-story stucco home in St. Paul with an annual income ranging from $16,000 to $30,000.

While their children have pitched in with income from part-time jobs, their family has had to rely heavily on financial support from relatives, friends, their church, and the state of Minnesota.

So important was that state aid that any reduction in the funding level meant a dramatic disruption in their lives.

John Roby recalled the time the state Supreme Court struck down the tax credit for private eduction. "We had to regroup and impress upon the kids that they'd have to work with a paper route or at the neighborhood bakery" to make ends meet, he said.

Lucille Roby said that even without the state aid, she would have tried to send her children to Catholic schools, but added, "Maybe we wouldn't have made it."

"Religious education is very important to us," she said. "We want to reaffirm what is morally acceptable in our family, and want it reinforced in the schools. So far we have succeeded."