An effort by a coalition of community and religious groups to persuade Congress to overturn a D.C. City Council measure that would legalize most homosexual acts will have its first test today on Capitol Hill.

The House District Committee will hold a hearing on a resolution by Rep. Philip M. Crane (R-Ill.) to kill the sexual liberalization measure.

A Senate Governmental Affairs subcommittee has scheduled a similar hearing next Wednesday on an identical resolution sponsored by Sen. Jeremiah Denton (R-Ala.).

A veto by either chamber of Congress would kill the council-passed bill.

The controversial measure, among other things, decriminalizes a number of heterosexual and homosexual acts, including sodomy, between consenting persons at least 16 years old.

The latest organization to ask Congress to overturn the measure is the mostly-black D.C. Federation of Civic Associations. In a letter to congressional leaders, its president, Arthur V. Meigs, attacked what he called the council's "steamroller legislative procedure . . . . "

The federation's mostly-white counterpart, the Federation of Citizens Associations, has voiced a similar position. The most publicized attack has been by Moral Majority president Jerry Falwell, who was joined by the D.C. Baptist Ministers Conference.

Catholic Archbishop James A. Hickey also attacked the bill, asserting in an open letter that many sexual acts legalized by the measure are immoral and "the withdrawal of civil prohibitions and penalties does not make them morally permissible."