An off-duty Arlington County policeman was fatally injured last night when the motorboat he apparently was operating collided with the Potomac River cruise ship Dandy just north of the 14th Street Bridge, D.C. harbor precinct police reported.

Police officials declined to identify the officer until family members could be notified. They said early today that they believe the officer was alone in the boat.

Investigators said the accident occurred about 9:15 p.m. as the Dandy was cruising down river at a speed of about 2 to 3 knots. They said that following the collision, the captain of the cruise ship, realizing that his crew would not be able to assist the motorboat operator, hailed the occupants of another passing motorboat and asked them to go to his aid.

The second boat then towed the boat with the injured officer to shore where a waiting U.S. Park Police helicopter took him to the Washington Hospital Center. He was pronounced dead there of multiple injuries about three hours later.

The cause of the crash between the officer's 26-foot boat and the Dandy, a 97-foot vessel owned by Potomac Party Cruises Inc. of Alexandria, was undetermined. The Coast Guard said it will investigate.

More than 100 persons were aboard the cruise ship at the time of the collision, police said, but apparently none was hurt. The Dandy sustained slight damage, while the motorboat was heavily dented on the right side, they said.