Martha M. (Bunny) Mitchell, a District of Columbia Democratic leader who recently was appointed a special assistant to President Carter, will have responsibility for coordination between the Carter White House and the District government.

Mrs. Mitchell, a 36-year-old black woman who last spring was chosen the District's alternate Democratic national committeewoman, said yesterday that serving as a D.C. liaison person on the President's staff will only be part of her job, but it's something she will have a special interest in.

Who represents the city's interests in White House discussions and how well he or she does it can be crucial to the metropolitan area. For example, city leaders credit Egil (Bud) Krogh, former White Hose aide under President Nixon, with playing a key role in winning administration support for financing the area's Metro rapid transit system.

In pasr administrations, presidential aides assigned to maintain liaison with the city have varied from those who have been so anonymous that officials in the District Building weren't aware when they left the job.

Mrs. Mitchell said yesterday that it is still too early for her to say how her District duties will be organized or how closely the Carter White House is going to pay attention to city affairs.

District leaders are anxious to have someone at 1600 Pennsylavania Ave. who can get a word with the President, especially in pleading for more federal funds for the city. But they are also anxious to avoid anything smacking of White Hose direction of an elected municipal government.

District officials expect shortly to be sidcussing with Mr. Mitchell and other White House staff members the best kind of working relationship between them. Mayor Walter E. Washington was not consulted before Mrs. Mitchell was appointed.

Mrs. Mitchell, a graduate of Michigan State University, has been chairperson of the D.C. Women's Political Caucus and on the D.C. Commission on the Status of Women. She was information director for the Drug Abuse Council in Washington.

Mrs. Mitchell is the second black women to serve in the White House with responsibility for liaison with the District government, Sally Anne Paton had a similar post under President Nixon.