Within days a thin volume outlining the major problems facing the District will be on its way to someone the contributors hope will be a sympathetic, interested reader: President-elect Carter.

The 50-page, confidential briefing book seeks to tell the incoming President th pros and cons of key issues affecting this federal city and which District matters require White House attention promptly after the Jan. 20 inauguration.

The outline and recommendations prepared for President-elect Carter stress the importance of carrying out his campaign promises to give the Districk greater home rule and revise the federal payment to the city.

The Carter briefing book also discusses what kind of coordination should be maintained between the White House and District government, local appointments the President-elect must soon make and in which ways the new administration can most help its home town.

The outline has been drafted by Leonard L. McCants, a 31-year-old Washington area lawyer and member of the city's Board of Zoning Appeals who has been working with the Carter transition team.

McCants' manuscript seeks to summarize the thinking of present and former city officeholders and other local leaders whom he interviewed for their advice.

McCants declined to make his draft available, but said in a recent interview that it discusses how President-elect Carter can move toward fulfilling his campaign promises of seeking to give the District greater home rule through "complete authority" over the city budget, local appointment of local judges and full voting representation in Congress.

McCants said all of the local leaders he surveyed were concerned that extensive press allegations of cronyism and mismanagement in the District government will hurt the city's chances of getting help from the Carter administration.

District leaders hope, McCants said, that the President-elect will view the problems of the District's Department of Human Resources and other city agencies as "entirely local matters which must be resolved by the local people."

McCants said his review recommends that President-elect Carter consider having the White House move to end its veto power over the city's budget, a presidential review that local leaders tend to feel is unnecessary and too time-consuming.

McCants said that District leaders are agreed that the federal government is going to have to come up with more money if the city is to avert financial crisis. The hope is that Carter will help persuade Congress to enact a more generous formula for appropriating the annual federal payment to the city government.

Two of the biggest financial headaches besetting the city are funding of its pension program and of the deficit-plagued Metro rapid-transit system. McCants' said his outline will urge President-elect Carter to push for as much federal assistance to complete the full, planned 98-mile subway system as is "practical and feasible."

McCants said District leaders privately expressed little hope that a so-called "commuter tax" will ever be enacted by a Congress in which the suburbs have voting representation and the city does not. Carter came out against a commuter tax during the campaign, McCants said, therefore, the emphasis in his report is, alternatively, on the need to increase the federal payment and other federal appropriations to the city.

The draft also urges the Carter White House to work toward giving the city the powers of taxation that states have.

McCants' manuscript reviews the past variations in White House-District government liaison which have gone from the days in the Kennedy Administration when White House aide Charles A. Horsky was considered by some as a "super-commissioner" of the city to what Districk leaders generally characterize as the "benign neglect" of the Ford White House.

Local officials interviewed by McCants are hoping that under President Carter there will be something between the two extremes. They want someone close enough to the President to be able to get his attention when the city needs help, but without having White House officials attempting to direct activities in the District Building.

City Council Chairman Sterling Tucker, one of those interviewed by McCants, favors having the District liaison person in the White House not merely be limited to District affairs, which could put him near the bottom of the office pecking order, but an aide with broad authority for urban problems while having a special interest in those of the District.

Tucker said that in his opinion Egil M. Krogh Jr., a White House aide under President Nixon, best represented the District at 1600 Pennsylvania Ave. Speaking of Krogh, Tucker said, "He was close to the top. He had enough access to have clout. If it weren't for him, we wouldn't have a Metro now."

McCants' briefing book lists the various judgeships and other local appointments that the new President soon will have to make, giving confidential assessments of various possible appointees. McCants was particularly tight-lipped about these, declining to give any hint of what his draft will recommend in regard to the reappointment of U.S. Attorney Earl Silbert.

The briefing book also discusses some of the unofficial but important things that a new President can do to help the city and himself politically here. President-elect Carter's enrollment of his daughter, Amy, in the District school system was noted by McCants as a move that has had a very good local effect.

Though President-elect Carter ran an anti-Washington campaign, McCants said, "He did not run against the local population. He ran against the federal bureaucracy."