It's not the kind of thing that topples institutions or breaks federal budgets, but Sen. Pete V. Domenici (R-N.M.) has worked himself into a small dither.

He is upset about free tickets being given away at the John F. Kennedy Center for the Performing Arts, which, at the same time, is asking for federal tax support.

Specifically, Domenici is talking about 28 cost-free admissions assigned to the White House, ostensibly for the president's use, and 12 more that go to center trustees.

Domenici yesterday introduced a bill that would sharply limit what the president does with his freebies when he decides to stay home.

The bill makes it plain enough: unless the president goes with guests, the tickets must be sold. Which means, apparently, that Rosalynn Carter pays if she goes alone. Hamilton Jordan pays. Jody Powell pays.

It's nothing personal, understand. It's just that Domenici is a bit bothered by the White House practice of passing out the freebies to staffers, legislators and their aides when the president stays home.

By the senator's calculations, the center is losing something like $175,000 a year by giving away choice seats to the White House and other aficionados of the arts.

Now, any senator would have to confess, a little largess isn't all that bad. About four years ago, Domenici and his wife, using freebies sent along by the White House, attended a ballet (he can't remember which) at the center.

But he says he feels it's another matter to be giving away seats and then turning to Congress for financial assistance. The bill also would eliminate the four cost-free seats held for trustees in each of the center's three major theaters.

"When an organization fails to meet its financial obligations, it is not wise policy, simultaneously, to give the product away for free," Domenici advised the Senate.

"Is that proper, when the center is crying for more taxpayers' dollars to pay expenses for parking bonds, for roof repairs, for heating, lighting and janitorial services?" he asked.

The fiscal 1980 budget would provide $4.3 million to help the center with security and cleanup. Slightly more than that has been spent to fix the leaky roof, and the center is talking about more federal money to insulate the garage.

Thomas Kendrick, speaking for the center, said Domenici's bill caught him by surprise. As for the "crying," he suggested that was the wrong word to apply to a cultural center that is basically supported with private money and which makes reducedprice tickets available to those who can't pay the full fare.

If Domenici's bill becomes law, the reduced-price tickets would continue. But the White House could no longer win friends and influence congressional staffers with those fetching invitations to sit free in the presidential box.