A number of special interest groups paraded before a Capitol Hill panel yesterday, asking the District of Columbia's congressional overseers to restore funds for their favorite projects in next year's city budget.

A parents' group wanted more money for the public schools, antiabortion proponents asked the congressional panel to prohibit the city from using local funds to pay for abortions for indigent women, and advocates for the mentally impaired demanded more money for Forest Haven, the city's home for the mentally ill.

The public hearings before the House subcommittee on D.C. appropriations was the court of last report for citizens to appeal Mayor Marion Barry's proposed budget for the 1982 fiscal year beginning in October. Congress still must approve Barry's budget, even though it has already been approved essentially intact by the City Council and cleared through the former Carter White House.

Recently, Congress has been giving the city more leeway in preparing its own budget, looking only at the overall budget and not the city's specific programs or priorities. This is a sharp break from previous years when Congress members pored over the District's budget line by line.

The parents' group, Parents United For Full Public School Funding, presented the panel with a survey, showing that the District spends less money on its public schools than does neighboring Montgomery County.

Although each school system serves about 98,000 students, the report said, Montgomery County spends $40 million more on schools, employs 350 more teachers, and spends twice as much on its school libraries as the District spends.

Barry's budget proposes $248 million for the school year beginning this fall, and the parents said that the system needs at least $27 million more. Peter Edelman, spokesman for the group, said, "Unless there's 275 million bucks there, we're going to see the kids come back to school this fall and face another tough situation."

Nellie J. Gray, president of the antiabortion group, March for Life Inc., told the panel that each year "about $1.7 million is used to kill about 6,000 innocent, preborn children in the District of Columbia." She said "the duty of Congress" is to prohibit the use of local or federal funds for abortions.

"Home rule does not mean 'local option to kill.' This is not a civil right. It is a crime against humanity," she said.

Leslie A. Harris, the executive director of the local American Civil Liberties Union, also testified on the abortion issue and urged the subcommittee not to adopt any antiabortion language. Such language, she said, "would encourage special interest groups . . . to bypass the D.C. Council and lobby directly before Congress."