TO AMERICANS, it must be deeply moving to hear of East German civil rights demonstrators gathered in East Berlin churches singing "We Shall Overcome." To the East German authorities, it must be deeply alarming to find themselves dealing with forces for change coming from both East and West simultaneously.

The state's latest collision with the civil rights movement was the attempt last month by unauthorized marchers to join the annual march commemorating the murders of Rosa Luxemburg and Karl Liebknecht, founders of the German Communist Party; the marchers wanted to carry a banner bearing a Luxemburg slogan, "Freedom is always only the freedom to dissent." That is not a congenial thought to the Communist bureaucrats who run East Germany.

They arrested some 200 demonstrators on that occasion. But the East German government has apparently become wary of the strains that it creates by holding these people in jail. It has now released nearly all of them, pushing about 60 quietly over the border into West Germany.

East Germany is a state under great pressure to change in ways that its government adamantly resists. For one thing, its people know much more about life in the West than does any other population in Eastern Europe. They can watch and listen to West German television in their own language. Some can travel. Until recently the authorities allowed only retired people, whom they consider a drag on the economy, to go abroad. But the rules have been relaxed, and last year more than 3 million East Germans, a million of them under retirement age, visited West Germany. That's an extraordinary number, in a country of 17 million.

But by no means is all of the talk of change coming from the West. The Gorbachev program and the talk of glasnost are clearly feeding a growing sense of wider possibilities among East Germans. The government, having held up the Soviets for decades as the infallible model in all things, is having trouble coping with the current talk in Moscow of reform.

The East German civil rights movement has not taken on the dimensions of the opposition in, say, Poland. It still seems to be generally confined to intellectuals, students and clergy. But it's also true that the East German state under Erich Honecker, now 75 years old, has had little experience with diversity or dissent of any kind. It seems to recognize that there is a spirit moving in the country that the state does not have fully under control.