Patricia Roberts Harris launched her campaign for mayor of the District of Columbia yesterday, telling supporters that her record as the head of two cabinet level federal agencies under President Carter is proof of her ability to outdo Mayor Marion Barry's "sorry performance" in office.

Harris, 57, was loudly cheered by an overflow crowd of more than 500 supporters at her campaign headquarters downtown as she accused the Barry administration of misusing the home rule government that the city had fought for and mismanaging the city bureaucracy.

"Today," she said, "less than eight years after home rule, we look to our local government and ask what has gone wrong. Instead of answers we get alibis. And chief among those who give us alibis instead of answers is the mayor who says he is not responsible for the failures of his government.

"If he is not responsible, who is? It's time that we put someone in charge of this city's government who won't be afraid to be in charge. I am ready to be a mayor with answers and actions--not alibis and apologies."

Leadership will be a major issue in the campaign, Harris said. "The central question is, which candidate will bring the most effective leadership to this city. I believe I am that candidate . . . . No other candidate has more experience in leading and managing organizations, both large and small. I know that I can do the job that so sorely needs to be done to put Washington D.C. on the right track again. You and I know that this election will not be an easy one. It's going to be a fight right down to the wire."

She brought laughter and loud applause from the crowd when she asked why Barry had waited until the 39th month of his term to announce a war on crime.

Harris said that if elected, she would place top priority on restoring faith in the competence of the government, producing a definitive and credible assessment of the city's finances, improving the city's working relationship with Congress and creating more jobs and job training here through better economic development.

She told those gathered shoulder-to-shoulder on the balconies of the K Street town house that is her headquarters that, as mayor, she would not raise taxes until her questions about the city's budget were answered.

"I do not believe that a mayor can, in good conscience, ask the citizens of this city for any new revenues until that mayor is satisfied that the fiscal accounting and budgeting practices of this city are sound," she said. "And I would not do so.

"Our public debate should be about how best to use the tools and resources we have available to make this city a better place, not how much money we have or where it is or where it is hidden. Let's stop playing games."

Harris' formal entrance into the race completes, at least for the moment, a crowded field of nine vying for the crucial Democratic nomination in the Sept. 14 primaries. The group includes Barry, D.C. Council members John A. Wilson of Ward 2, Charlene Drew Jarvis of Ward 4 and at-large members John Ray and Betty Ann Kane. Also in the race is physician Morris Harper, publisher and businessman Dennis Sobin and artist Richard Jackson.

Yesterday Harris was introduced by Sharon Pratt Dixon, the city's Democratic National Committeewoman, who is director of the Harris' campaign. Dixon and Charles T. Duncan, who served as the city's corporation counsel under former mayor Walter E. Washington's administration and is treasurer of the Harris campaign, stood behind the former secretary of Housing and Urban Development and Health and Human Services as she spoke.

Among those in the crowd at yesterday's campaign kickoff were school board member R. Calvin Lockridge from Ward 8 in far Southeast Washington, who has been a key adviser to the Harris campaign; at-large board member Barbara Lett Simmons; and Pat Press, a real estate agent who ran unsuccessfully for D.C. Council in Ward 6 in 1978.

Also on hand were Mary Ann Keeffe, who lost the Ward 3 race for school board last November; Vicki Street, former Ward 4 representative to the school board; Douglas E. Moore, a former at-large member of the D.C. Council; Ann King, head of government relations for the AFL--CIO; several dozen members of the Delta Sigma Theta sorority that Harris belongs to and groups of people who worked with Harris when she was a member of Carter's cabinet from 1977 through 1981.

"I didn't know if she had the organization to win," said Moore, who now is running for the council seat from Ward 5. "But after seeing who is here, today I can see she has got the horses. The horses are here and they are ready to run."

Early polls of candidate popularity have suggested that Harris could pose the toughest challenge to Barry, if, observers have cautioned, she can develop an organization. She raised $80,000 for her campaign in slightly more than a week before the March 10 deadline for reporting campaign contributions, and after her speech yesterday she said that the heavy turnout of supporters, despite an off-and-on morning rain, reassured her that her campaign is organized well-enough to win.

"These people," Harris said, "were here without anyone promising them a job or threatening to take away somebody's job."

Last week, after opening her headquarters, Harris said her campaign manager will be Arthur Murphy, who was deputy campaign manager for Charles S. Robb in his successful bid last fall for governor of Virginia. Murphy's main aide for fund raising is Joyce Seigel, who organized a $25 a plate dinner last night for Harris at the Women's National Democratic Club on New Hampshire Avenue.

"We've said to ourselves that we've got to have the money we will need to win by Aug. 15," said Henry Hubschman, Harris' former executive assistant who is now involved with fund raising for her campaign. Harris aides estimate that the campaign will need $500,000.

"You know you are going to have a slow period for giving after June 15 when the summer starts so you have to anticipate that," Hubschman said. "We're looking at that kind of thing now, but by any measure we are doing better at fund raising than anyone expected . . . and 90 percent of our money is coming from inside the city."

In an interview last week Harris portrayed herself as an underdog in the campaign. But she said she was confident she could win, despite criticism from some of her opponents that she has not been involved with local government, is out of touch with the city's poor and was holding prestigious jobs in government at a time when others like Barry were in the front lines of the civil rights movement.

"Oh, they weren't on the front lines," Harris said. "They were there when it was safe. When the television cameras were there. I was there when there were no television cameras."

Harris said criticism of her record of local involvement was being made by people who are either too young to remember what she has done in the city or are purposely trying to ignore her work.

In addition to having been elected the Democratic National Committeewoman from Washington in 1976, Harris said she has served as chairperson of the D.C. Law Revision Commission, sat-in to integrate an all-white cafeteria on 14th Street in 1943, been vice-president of the Brookland Civic Association and chairman of the Washington Urban League's housing and welfare committees.

"Now how much do they want," she asked. "Now I am willing to bet you if you put that list of what I was doing at the time I went into the cabinet next to my opponents it is probably longer than what they are doing now or have done outside of their political activity. And none of what I did was for the purpose of running for office."

Harris' campaign literature distributed yesterday trumpeted community involvement as one of her attributes, along with leadership and management, at HHS, of "the world's third largest budget" (after the United States and the Soviet Union).

Harris has been meeting with small groups of city residents since late December when she said she was considering running for mayor. Those musings ended Feb. 24 when she filed as a candidate for mayor.

Harris said in an interview that her campaign will continue to feature those meetings because she will not attend forums where candidates are allowed to make only short statements because she thinks that would be useless.

Harris campaign strategists, like those for other candidates, say that because so many candidates .re in the race, a large plurality, not a majority, of the votes cast can lead to victory. Also like the others, they lay claim to areas won and lost by Barry in 1978, when he eked out a victory with 35 percent of the vote in a close three-way primary.

Harris' strategists expect the core of her support to come from older, middle-class, well-educated and moderate blacks who favored former mayor Washington and former council chairman Sterling Tucker over Barry in 1978.

Many of those people live in Ward 4 in upper Northwest Washington and Ward 5 in Northeast Washington, the two largest Democratic wards in this overwhelmingly Democratic city.

Those close to Harris also expect her to run well among working-class people in Ward 6, which includes Capitol Hill, near Northeast Washington and parts of Anacostia, and in Ward 8, which also includes Anacostia and other parts of far Southeast Washington.

Harris strategists also said they expected her to do well in Ward 3, the area west of Rock Creek Park, where Barry did best in 1978 but has acknowledged losing some support since taking office.

Harris, who was born in Matoon, Ill., came to Washington to attend Howard University. After she graduated in 1945, she worked for the YWCA in Chicago and then returned here in 1953 to be executive director of Delta Sigma Theta.

She received her law degree from George Washington University in 1960 and a year later, became a lecturer in law at Howard University. After serving as part of the city delegation to the 1964 Democratic Convention, she served as U.S. ambassador to Luxembourg and later a deputy U.S. delegate to the United Nations.

She became dean of Howard Law School in 1969 but quit a short time later in a dispute with the administration. She then went into private practice with the firm of Fried, Frank, Harris, Shriver and Kampelman before joining the Carter cabinet.