TODAY WE WANT to talk about the Washington Jimmy Carter didn't campaign against - the one we all live in. We have some thoughts on the kind of relationship the Carter White House should try to work out with the city. Mr. Carter does seem to be interested in establishing some genuine ties with his new home away from home. As everyone knows, the Carter are already in the process of affiliating with the D.C. public schools and having the neighborhood churches checked out for future visits.

These are surely good and benign signs. Many a past President, of course, has arrived expressing at least some perfunctory interest in his new surroundings. There was even one recent President, Mr. Nixon, who, having so kindly tagged Washington the "crime capital of the world," took to the sidewalks of 7th Street NW only days after he was installed in office, to make a pitch for immediate rebuilding of the riot corridors. Alas, the main thing Mr. Nixon built in this city before he left was the national name recognition of one of our largest hotel-office building complexes. Still, quite aside from traditional presidential overstatements of interests in this city, the need exists for some sort of special liaison between the District and the White House. And this has been formally recognized ever since the Kennedy administration.

President Kennedy named a special assistant for national capital affairs. This role was properly altered when President Johnson reorganized the District's government into an appointed commissioner-"mayor"/city council system. To shift more of the decision-making to the District Building, Mr. Johnson eliminated the specific local position in the White House, he also diminished greatly the amount of detailed attention that the then-Bureau of the Budget had been giving the city's policies and finances. President Nixon at first placed District affairs under his presidential adviser on urban affairs, and later with his Domestic Council staff. These staffs focused on specific issues, such as crime control, the federal payment and financing for the Metro system. Under President Ford, nobody in the White House has ever been caught devoting any significant time to District matters.

So the first thing to say Mr. Carter is that if he does intend to establish some formal liaison with the community, he shouldn't follow the patterns or precedents of the past. For one thing, the existence today of an elected city government with increased authority over municipal affairs makes a difference. In fact, there shouldn't be a high-level presidential adviser on District affairs. The city's leaders, now accountable to constituencies, ought not be constantly overshadowed or undercut by some presidentially appointed District "czar."

Instead, the task of following local affairs should be assigned to a person or staff responsible generally for national urban policies. Specific District matters that merit President Carter's personal attention could perhaps be channeled through Vice President Mondale if he really continues to have the President's ear. He knows this city well and is most sympathetic to its special needs. Such an arrangement, coupled with a direct working relationship between those responsible for District matters and the administration's congressional liaison staff, could provide an effective system by which Jimmy Carter could do his new local government some good.