Mayor Marion Barry and his wife Effi are suing a Southeast Washington couple for a total of $2 million in damages over neck and back injuries that they claim Mrs. Barry received in an accident on New York Avenue in February 1984.

In a suit filed this week in D.C. Superior Court, the Barrys contend that Mrs. Barry was seriously injured when a chauffeur-driven unmarked police car she was in was struck from behind by George Nelson, 63, a disabled laborer.

The suit seeks $500,000 in compensatory damages and $500,000 in punitive damages each from Nelson and his companion, Rosa Samuel, who owns the car but was not present during the accident.

The mayor and his wife contend that, as a direct result of the accident, they have "suffered the loss of society, companionship and consortium of each other."

Vertice J. Gore, a D.C. police officer who was driving Mrs. Barry and who suffered a hand injury in a scuffle with Nelson following the accident, also has sued Nelson and Samuel, seeking a total of $1.5 million. Gore and his wife, Joyce, claim that Gore suffered injuries and damages "consisting of, but not limited to, cervical strain."

Nelson, who lives on $323 a month in Social Security benefits, and Samuel, a 53-year-old cook, said yesterday they were stunned by the lawsuit.

"No sir, there is no way I could pay," said Nelson, who lives in the 5000 block of Bass Place SE. "I don't have nothing, and all this child [Samuel] has is a little bit."

Samuel, who lives in the 5000 block of Central Avenue SE, said that she was at work when the accident occurred and is troubled that she was named as a defendant.

"It's got me upset," she said. "I'm laying down in bed. I'm trying to go to work but I'm upset. I don't want to lose my home."

Samuel said that she has some insurance coverage with the Universal Insurance Agency Inc., but not nearly enough to cover the damages being sought.

Barry left town yesterday on a four-day vacation and was not available for comment. Effi Barry, reached at a local advertising firm where she works, referred all questions to her attorney and said it would be inappropriate for her to comment on a pending lawsuit.

Ronald A. Karp, a lawyer for the Barrys, said Mrs. Barry was badly shaken in the accident, adding, "She was really given a shot."

"Essentially, the mayor and his wife have the same right" to sue a driver as anyone else in the District, he said.

The accident occurred the afternoon of Feb. 8, 1984, as the unmarked car carrying Gore and Mrs. Barry traveled east on New York Avenue near the intersection with South Dakota Avenue NE.

According to police, the unmarked car was struck from behind by a 1977 Dodge Aspen driven by Nelson. Mrs. Barry, who has suffered from a spinal disk ailment, was wearing a neck brace at the time.

Mrs. Barry was taken to Providence Hospital complaining of neck and back pains. She was released to the custody of her family doctor about two hours later.

According to the lawsuit, she suffered injuries including "acute cervical, dorsal and lumbar strain and exacerbation of pre-existing radiculopathy." As a result of those alleged injuries, the suit said, Mrs. Barry suffered a loss of earnings and "great pain of body and mind."

Police said that when Gore tried to prevent Nelson from leaving before a D.C. traffic division cruiser arrived, he was assaulted with a screwdriver and a fight ensued.

Nelson, who was later convicted of driving while intoxicated and lost his license for six months, said yesterday that he was driving no more than 10 mph in congested traffic when his car hit the police car. "I didn't see any damage," he said.

He acknowledged that he "scuffled" with Gore when the officer tried to prevent him from leaving. Nelson said he was struck on the head by either Gore or another officer and that it took eight stitches to close the wound. Nelson denied assaulting Gore with a screwdriver and noted that authorities later dropped an assault charge against him.