A District of Columbia policeman in his private car exchanged several shots with occupants of two other cars in a brief but wild chase through northwest Washington yesterday that ended with the arrest of two men. There were no injuries.

Police said the incident started about 10 a.m. when two men who had just completed a crap game in the 400 block of M Street NW were held up at gunpoint by a third man.

Taking $95 in cash, the man jumped into a waiting car occupied by a companion and sped away, police said. The two victims hailed triends in another car and began chasing the first car, according to police.

As the two cars sped through the Shaw area of northwest Washington, several shots were exchanged, police said.

Officer Randell Ramey, a third district policeman dressed in civilian clothes, was driving to court in his car, when he spotted the speeding autos. He fell in behind them, also firing several shots, according to police.

Ramey finally stopped one of the cars in the 1900 block of 14th Street NW. Special operations division officers, who had joined in the final moments of the chase, cornered the second car with their police cruiser in 2100 block of 12th Street NW, police said. The occupant surrendered with out struggle.

Arrested in the second car on 12th Street and charged with armed robbery, according to police, was Carl S. Lucas of St. Michaels, Md. A second suspect, identified by police as Perry Maye of 439 M St. NW, was arrested in the first car on 14th Street and charged with assault with a dangerous weapon. The other occupants of the cars were released.