THE HOUSE Appropriations Committee, which reviews the District's budget tomorrow, should restore the portions of the city's budget cut several weeks ago by Rep. William Natcher (D-Ky.). Mr. Natcher, Appropriations subcommittee chairman for the District, unexpectedly slashed nearly $80 million from the 1979 request, including $53 million from the federal payment alone.

The cuts were capricious as well as substantial. One deleted item would have created a more efficient method of collecting parking fines, with an estimated revenue gain to the city of $20 million. The subcommittee wiped out a $1-million fund to help lower-income residents make down payments on their homes. Half the money requested for advisory neighborhood commissions was cut; more than 200 new staff positions were eliminated. As for the money the federal government pays to the city to cover the cost of local services, both the City Council and the White House have been trying to increase a that payment. Instead, Mr. Natcher approved a federal payment of $53 million less than city officials requested and $12 million less than Congress gave the District this year.

Mr. Natcher's action was prompted, at least in part, by a desire to eliminate waste and duplication in the District government. Undoubtedly he figured that a drastic cut would force local officials to tighten their belts. In one respect he is correct: There is inefficiency at city hall - even District government officials admit that. In the past several months, city officials have begun making some internal changes on their own.

But our main objection to Mr. Natcher's recommendation lies here. He has taken upon himself the job of every local government of deciding how specific programs should be adjusted in the face of budget cuts. While Congress has the right to determine just how much federal money the District should receive, local officials should be the ones to figure out the least harmful way to trim the budget. Mr. Natcher has done more than confuse local planning. All by himself he has, informally but effectively, abridged District self-rule. The House Appropriations Committee should not let Mr. Natcher have the final say.