COLUMBIA, Mo. (AP) _ The Justice Department has agreed to investigate incidents of alleged brutality against blacks by members of the Columbia Police Department.

The investigation of the incidents, the latest on Dec. 25, was requested by Mary Ratliff, president of the Columbia chapter of the National Association for the Advancement of Colored People.

Bill Whitcomb of the Justice Department's Community Relations Service said he will meet Monday with Police Chief Bill Dye and members of the NAACP to provide ''mediation and assistance.''

The Dec. 25 incident began when police tried to stop Glenn Cobbins, who had halted his car to talk to someone, for obstructing traffic.

Cobbins, 25, who was paid almost $6,000 in damages after he was shot and wounded by a Columbia police officer in 1979, drove off and went to his home.

There was a melee involving members of his family as police tried to arrest him, and four people, all of them black, were taken into custody.

One of them, Anna McPhatter, 39, of Woodridge, Ill., resisted when police tried to photograph and fingerprint her.

''She is a peaceful person,'' said Ms. Ratliff. ''Yet she was treated like a common criminal. The atitude on the part of the police is that everybody in that area is black, so everybody has a problem down there.''

Dye, who is black, contended his officers acted properly.

''I don't see any harassment here, at least not as I understand harassment,'' he said. ''I see the word brutality used. Nobody has been hospitalized. Nobody has been injured.''

The other incidents the NAACP asked be investigated included one on Oct. 16, when police subdued a woman who threatened them and neighbors with a 15- inch knife after she fought with her boyfriend.

Dye said the woman, Evelyn Daye, had a deadly weapon and that an officer bent her thumb back to force her to drop the knife. He said domestic squabbles are often volatile situations presenting a potential for injury or death to police officers, and that he believed the Oct. 16 incident was handled properly.

The third incident happened Dec. 10 when police chased Jeffrey Hayes and caught him at his mother's home. Police said Hayes matched the description of an armed robbery suspect and that he ran away from an officer.

Hayes was later released because he had nothing to do with the robbery, police said.

Dye said the incidents involving Hayes and Cobbins are being reviewed by his department.

When Cobbins was 18, he was shot and wounded by Columbia Officer John Cunningham. In July of 1979, police had responded to a report of auto tampering and saw Cobbins running from the area, and Cunningham fired two shots, hitting Cobbins in the foot.

In a settlement stemming from the incident, the city paid Cobbins $4,750 and Cunningham paid him $1,000.