Three robbery suspects were arrested in the District yesterday after a wild pre-dawn auto chase that began in Rosslyn after a holdup at a hotel and roared for miles at high speed through South Arlington and Alexandria, authorities said.

The chase, at speeds reaching 90 miles and hour, ended about 5 a.m. when the gold 1969 Cadillac being pursued ran off Thomas Circle NW. hit a tree and burst into flames, police said. No injuries were reported in that collision.

Earlier in the chase, two Arlington policemen were injured when they swerved to avoid a citizen's car and lost control of their cruiser, which struck a tree in the 3200 block of S. Glebe Road, police reported. The officers, Michael Lewis and Richard Ault, were treated at Arlington Hospital and released. Their cruiser was demolished.

Police said the incident began about 4:30 a.m. when three men, claiming to be security officers, knocked on the door of a room in the Ramada Inn at 1900 Ft. Myer Dr. in Rosslyn.

When the door was opened, the men - one armed with a knife - entered and grabbed the occupants, Laurie Sue Priest, 22, of Bixville, Ohio, and Maryanne Dempsey, 22, of Kenilworth, III, according to police. Priest suffered a knife cut in the struggle, but was not seriously injured, police said.

The women, were to enroll in a special course at American University, were tied up, and the robbers took money and fled.

The women freed themselves and called police, who found three men in a Cadillac near the hotel and began questioning the driver. Suddenly, police said, the car drove off at high speed and the chase began.

After heading south into Alexandria, the chase continued on Shirley Highway and cross the 14th Street Bridge. On the bridge the Cardillac sideswiped a police car attempting to cut it off. Damage was minor.

After the Cardillac crashed on Thomas Circle, three men were pursued on foot by D.C., Arlington and U.S. Park police.

Police said they arrested Zachary Tyrone Millie, 19, and Ernies T. Russell, 18, both of 828 Otis PL. NW. and Tyrone M. Jefferson, 19, of 1205 Harvard St. NW. All were held last night in Arlington on charges of armed robbery, felonious assault and kidnapping, authorities said. Arlington police said the binding of the women gave rise to the kidnapping charge. All three suspects waived extradition proceedings.