The coalition of civic, business, religious and labor groups that successfully guided the District of Columbia voting rights measure through Congress is on the verge of dissolution in a power struggle with the city's three chief elected officials.

The two paid staff members of the Coalition for Self-Determination, formed by 50 national organisations in 1971 to seek home rule for the District, resigned yesterday amid charges of bossism directed at Mayor Marion Barry, D.C. Del. Walter E. Fauntroy and City Council Chairman Arrington Dixon.

Coalition employes Elena Hess and Melanie Woolston said they quit after the newly formed D.C. Voting Rights Service Corporation, created by the three public officials, failed to pay their salaries. During this time, the corporation hired a lawyer, recommended by Fauntroy, to serve as executive director, at $72,000 a year.

Attorney Joseph L. Rauth, treasurer of the coalition, told Fauntroy, that "we are confronted with the resignation of the two most valuable assests" of the coalition "because you didn't live up to your commitment to work together as equals."

Rauh said he was absolutely flabbergasied" that the two women had not been paid Rauh said the coalition called off its own fund-raising plans when the corporation was created in April pay, totaling about $4,000, last Tuesday. The coalition will pick up their salaries for the first half of May.

Rauh charged that Fauntroy "presented us with an ultimation. That's not a way to work together, it's a way for you to take over," Rauh said the coalition was "prepared to give a lot, but you'll have to make some movement too."

Dixon said legislation creating the corporation was approved by unanimous vote of the City Council. "Walter Fauntroy was not the mover, designer, promoter," Dixon said. The coalition is applying "an old, overused, improper idea of boss" to the elected officials, Dixon added.

The mayor, who confessed he was "getting short-tempered" about the infighting, said he was "confused about the continued discussion about who gets credit" for the compaign. Meanwhile, Barry added, "we're faltering, and our opponents get organized with resolutions of disapproval."

Rauh, who said he has worked 33 years for voting representation in Congress for District residents, proposed a compromise between the warring groups, explaining, "I want this (ratification) very bad, before I conk off."

Further haggling about who will control the ratification campaign "could kill it," Rauh warned. "We haven't done well so far," he went on, noting that "all of the successful amendments to the Consitution had at least half" the states required for approval at a similar point in the seven-year ratification period.

Since it was approved by Congress last August, six legislatures have ratified the amendment and 10 others have rejected it. To become part of the Consititution, 38 states must approve it by mid-1985. It would give the District two senators and one or two House members. Now, Fauntroy is nonvoting delegate in the House.

Richard W. Clark, the Common Cause lobbyist who has been working full time with the coalition, said he calle yesterday's meeting to attempt to resolve the dispute between the coalition and the corporation. He told the particpants, "Don't hold your punches, don't continue the charade" of cooperation between the competing groups.

At the end of the 2 1/2-hour meeting at Common Cause headquarters, Clark said the compromise amounted to "a de facto decision to disband" the coalition.

The compromise calls for the two groups to attempt to resolve their differences, with a goal of making the coalition a full partner in the corporation.

Clark said he personally has "strong reservations" about joining forces with the corporation, saying he questions its approach, management and financing. He said several organization within the coalition also are reluctant to be associated with a group headed by three Democratic politicians.

"There is not a ghost of a chance" of raising the $1 million a year proposed by the corporation, Clark said. He predicted potential donors would be scared off by "the quarter of a million dollars in overhead."

Harry Teter, finance officer of the corporation, said yesterday that the organization has $20,000 monthly budget. Of that, $6,000 goes to the law firm of Hamel, Park, McCabe and Saunders, which in turn is providing Anthony J. Thompson as executive director of the corporation. Thompson said the $72,000 fee includes his salary "and other legal services."