More than half the female State Department employees in a survey said they were harassed sexually at work, giving the department the worst record in a study of the problem in the federal workplace.

But the department is by no means alone in having a dismal record. The survey by the U.S. Merit Systems Protection Board said sexual harassment is "pervasive, costly and systemic" in the federal workplace.In a report issued Wednesday, the board said 42 percent of women and 14 percent of men who responded to its survey of federal employees experienced some form of sexual harassment from May 1985 to May 1987. That figure was virtually identical to findings in its 1980 survey.

The board found that the problem cost the United States an estimated $267 million over the two-year period in paying sick leave to employees who missed work, replacing employees who left their jobs and in reduced individual and group productivity.