Maybe you've been hearing it, too: someone (the rumor goes) has been telling voters that if the tuition tax credit passes next week, you will get $1,200, in cash or check, for each of your children. You're supposed to spend the money on private-school tuition, of course, but if you keep a little back for other purposes, well, who's to know?

Maybe someone has been spreading this vicious bit of misinformation. But you can't prove it by me. I've just made three hours' worth of random phone calls to Ward 8 residents, where, according to the rumors, the $1,200 misunderstanding has been chiefly fostered, and I found not a single voter who had heard it.

It's worse than that: several dozen phone calls did not succeed in turning up a single voter who knew in any but the vaguest terms what the tax credit initiative was about. Some thought it might have something to do with college tuitions; others flat hadn't heard of the proposal, though most of them did seem interested. Only four of those I reached said they intended to vote next Tuesday; two of those said they were registered.

I don't know what to make of these decidedly unscientific findings except to guess that the tuition-tax-credit issue--arguably the most significant issue to come before District voters since Washington gained the right to vote--will be decided in the middle- class precincts, where the pocketbook interest is greatest and the need is least. In one modest-to-low-income part of Southeast, the controversial initiative appears to be a non-issue.

And yet it is the low-income parents on whose behalf the backers of the initiative claim they are working. Their whole point, they argue, is to give parents of modest means the same public school/private school choice already enjoyed by the middle class.

It's no easier to guess how the middle class will vote on the issue. Most of the interview stories in the paper indicate that they will vote against the initiative, on the ground that its passage could do severe damage to the public schools. But I've been talking to some middle-class parents of private- school children who say they will vote yes. Since the public schools are hopeless anyway, they say, they might as well vote their own financial interest. They'll take the $1,200, which they see as free money, without guilt.

Well, it's not exactly free. If the measure becomes law, one of two things will happen. 1)A large number of public-school parents will opt for private or parochial school, in which case the city treasury will lose $1,200 per child, forcing the closing of a large number of school buildings and the firing of a large number of teachers. If the parents then find that the $1,200 is insufficient to meet the cost of nonpublic education, or if they find that the private or parochial schools are unsatisfactory, there will be no public schools for them to return to.

That probably won't happen, for the simple reason that there aren't enough vacant private school spaces to handle a large influx, which means 2)the chief beneficiaries of the credit will be those parents of the 20,000 children already in private schools. And that means that the city treasury will be short $24 million, right off the top. In that event, Mayor Marion Barry already has indicated, he will have no choice but to raise real-estate taxes by enough to make up the slack. Thus the money the initiative puts in one pocket, property taxes will take out of the other.

Incidentally, the passage of the initiative won't mean $1,200 in the pocket for any except those taxpayers who earn enough to pay at least $1,200 in city taxes (that would require an income of $25,300 a year for a family of four) and itemize their tax returns.

The initiative would not give you $1,200 in cash. It would only reduce the amount of city taxes you owe by that amount--or whatever amount less than that you spend on private-school tuition. If you pay no local income tax, you get nothing.

One argument in support of the initiative is that private-school parents pay twice for their children's education: once in their private-school tuition and a second time in the portion of their taxes that supports the public schools. To the extent that having their children in nonpublic schools relieves the city of the necessity of educating them, shouldn't they be entitled to a refund?

One woman who has heard the argument offers this response: "Say I have only one child in school, and I pay exactly $1,200 in city taxes. Since the initiative would give me a 100 percent refund of my taxes, who pays my part of the taxes that are slated for street repair, Metro subsidies, building inspection, public health services, spraying and replacing trees, plugging up burst water mains, hauling sewage waste to distant dumps and treating the Potomac water so it is fit to drink?"

Good question.