The House of Representatives has voted to exempt a Capitol souvenir shop from the District's sales tax, in the latest round of a home-rule battle that both sides say outweighs the $740,000 tax bill involved.

For the District, the issue is its power to tax without congressional interference. But sponsors of the exemption argue that the foundation of Congress' power rests on the fate of the small souvenir stand.

In the middle is the U.S. Capitol Historical Society, which has run the shop since 1964. The District in 1979 told the society it would have to start paying city sales tax on the nonhistorical items it sells, and that in fact it was already liable for $740,000 in back taxes for its commercial sales since 1966.

The District sued for the back taxes , but lost the case in U.S. District Court in September after the U.S. Justice Department argued that the society is an instrumentality of the federal government and therefore not subject to local taxes. The city has filed a notice of appeal.

Meanwhile, the society's congressional supporters put the exemption bill on the calendar for noncontroversial bills. and the House approved it Monday.

The appearance of the bill on the agenda surprised the staff of the House District Committee, which thought the legislation was being held pending court action.

"I think there is a good chance that the District can win the appeal," said Johnny Barnes, staff counsel of the committee. The souvenir shop competes with local merchants on such items as cameras and film, and therefore should pay the tax, Barnes argued.

But those pushing for the exemption say that only Congress has authority over its own physical home at the Capitol. Furthermore, they argue, it involves constitutional issues as recognized in proclamations dating back to George Washington.

The exemption bill has been referred to the Senate Government Affairs Committee and may be taken up by the Senate during the current session.