Mary Catherine Murtagh, 38, a director of liaison for the Office of Technology Assessment in Congress, died Monday at George Washington University Hospital following a stroke.

Miss Murtagh began her career on Capitol Hill in 1970 as an aide to Sen. Edward M. Kennedy (D-Mass.). She had been a volunteer in his 1970 campaign for reelection to the Senate, and in 1968 had been a volunteer in the campaign of the late senator Robert F. Kennedy (D-N.Y.) for the Democratic nomination for the presidency.

She was named director of liaison in the OTA, which provides Congress with advice on technical questions, in 1977. Sen. Edward Kennedy is a founder of the office and is one of its alternating chairmen.

Miss Murtagh was born in Detroit and graduated from the University of Detroit in 1962. She worked for the Social Security Administration in Detroit, New York and Baltimore before moving here.

While working for Sen. Kennedy, Miss Murtagh earned a law degree at Eorgetown University by attending night classes.

She was a member of the D.C. Bar, the American Bar Association, and the American Civil Liberties Union.

Survivors include her mother, Anna Murtagh, of Southfield, Mich., and a sister, Margaret Ann Barylski, of Dearborn, Mich.

The family suggests that expressions of sympathy be in the form of contribution to the Community for Creative Non-Violence, 1329 N St. NW. CAPTION: Picture, MARY C. MURTAGH