David Cohen, president of Common Cause since 1975, has told the organization's board of directors that he will resign at the end of his term in April.

Cohen, only the second president tht the nonpartisan citizens' lobbying group has had, said he is leaving because of a need for both personal and institutional renewal.

He became president of Common Cause in 1975 at a time when many of the changes recommended by the group were being adopted as law, following the resignation of Jack Conway. In November, Cohen told board members he had decided to leave.

Yesterday Cohen said he does not know what he will do when he resigns but hopes to continue to work in the nonprofit public interest area. "I want to keep working on issues and efforts to link the activities of the 1960s and 1970s and efforts that make sense for the 1980s," he said.

A search committee headed by Common Cause Chairman Archibald Cox will choose Cohen's successor. One candidate is Fred Wertheimer, senior vice president of Common Cause, whom Cohen has recommended.

Cohen's departure comes at a time when the movement of those who say they champion the public interest is in less than full flower.

"I do have a worry about the public interest movement based on conversations I've had," Cohen said in a recent interview with Common Cause's magazine. "Someone came up to me after the elections and said, 'My God, you should call everybody together and see what we can do,'" sounding as if Ronald Reagan were Ghengis Khan."

"There's a real danger that people in the public interest movement will continue to scream to the heavens that the 'sky is falling' and that that will become a substitute for trying to work through new ideas and new coalitions," he said.

Cohen said yesterday that in a trip to the West Coast he has found substantial energy and enthusiasm for government reform and citizen action, "a nonwithdrawal mood," he said. "The handwringing in Washington is the opposite of the sense of exploration and the sense of battle, as well, out in the country."