THE TUITION TAX CREDIT, a bad idea that President Reagan now reportedly intends to revive, has a certain melancholy perfection to it. This tax credit is bad law, for it probably would infringe the Constitution. It is bad economics, for it would create another large tax subsidy and add to the budget deficit. It is bad public policy, for it is an assault on the public school that, for most American families, is a center of community life.

What's to be said in behalf of the tuition tax credit? Not much, except that many parents with children in private or parochial schools would like the federal government to help pay their tuition. Mr. Reagan is apparently about to propose contributing $500 per child through the simple device of letting the parents take that much off their income tax payments--with the inevitable cash pay-out to those whose taxes aren't that high.

When people are unsatisfied with public services, they have an unchallenged right to set up their own parallel services privately. If you don't want to use the city swimming pools, you can build your own. But you aren't entitled to public funds to help you pay for it. If you think that the police protection is inadequate, you can hire your own watchman. But you can't reasonably ask for tax money to pay him. The same rule applies to schools.

It applies with special force to those schools that have been established for religious purposes, to provide children with a kind of education that the public schools must not offer. A tax credit of $500 is a direct payment to a parent, just like a check for $500 from the Treasury. A federal payment to a parent to provide religious training for a child raises an issue on which the First Amendment is pretty clear.

The cost of this subsidy would be something over $2 billion a year. By an illuminating coincidence, that is just about the amount by which Mr. Reagan has proposed to cut federal spending on education next year. With the tuition tax credit, he would alter his budget significantly. It would mean that he was no longer cutting federal funds for education. He would only cut spending on public schools, and on aid to college students. Instead, he would swing those billions of dollars to support of the private schools. Aside from any other aspect of this unhappy venture, is there anyone in Congress who thinks that Mr. Reagan and his budget have $2 billion to spare for this purpose?

But there is much more at stake here than money. The tuition tax credit would be a powerful subsidy, encouraging private schools and eroding the public ones. Whatever their shortcomings and exasperations, the public schools are among the most valuable and productive of this country's institutions. They are central to the way the country works. They are the places where most Americans learn the meaning of opportunity, equality and democracy. To the extent that the Reagan administration weakens the public schools, it will have weakened--inadvertently but inevitably--the values for which it stands.

Mr. Reagan has not yet publicly committed himself to a campaign to get this tuition tax credit through Congress. He still has time to reconsider.