A Hyattsville couple and their son have won an out-of-court settlement of $600,000 plus a minimum of $40,000 a year for the lifetime of the boy, who was born severely brain damaged at Providence Hospital in 1980.

Arlene Burnes Morgan contended that her son was born with multiple handicaps because doctors at the hospital in Northeast Washington failed to heed her concern that the baby was nearly two months overdue and appeared to be showing signs of distress inside the womb.

Morgan, who was 30 at the time, said in an interview that her private physician, J. William Costello, told her to expect her first child, later named Robert, on July 23, 1980, and that in June 1980, Costello referred her to the Center for Life Clinic at Providence Hospital, where her care would be less expensive.

At the center, Morgan said she was seen by Dr. Gabor Laufer, a resident, and Dr. Serge D. Rameau, who, along with the hospital, were defendants in the suit. Costello was also a defendant originally, but Morgan later dropped the complaint against him.

Lawyers representing both the hospital and Laufer refused to comment on the settlement. Kenneth Armstrong, attorney for Costello, confirmed the settlement and said the payments would be shared equally by the hospital, Rameau and Laufer.

David Levin, the attorney for Rameau, said yesterday the malpractice action was settled not because the doctors believed they had done anything wrong, but "because of the severity of the injuries that the child sustained." Levin said that the doctors contend that the baby was not a month overdue. Levin said the doctors believe Morgan's estimate of when she stopped taking birth control pills and became pregnant was about a month off, making the baby due near the end of August instead of the end of July.

Morgan's due date came and went, and according to her attorney, Edward Horowitz, tests performed at the hospital in mid-August suggested that the fetus was mature. Horowitz said doctors at Providence tried unsuccessfully to induce Morgan into labor on Aug. 28 and 29, and when that did not work, Morgan was sent home.

"The next day I didn't feel Robert moving," Morgan said, recalling that she was nearly hysterical because she feared her child was dead. Morgan said that she called the hospital, but was told not to worry.

On Sept. 13 she went into labor for a short while and was sent home, only to return a few hours later, in labor again, Morgan said.

"This time the monitor tracking the baby's heartbeat went berserk," Morgan said. Four hours later, according to Horowitz, Laufer and Rameau, after consulting with the chief of obstetrics, delivered the baby by cesarean section.

Morgan said tests later found that the child had microcephaly, meaning that his brain and skull will not grow beyond their infant size. She said he is severely retarded, does not have control of his legs and arms, and may never walk, talk or feed himself.

Morgan, a former meat cutter and receptionist, said the settlement will enable her to hire a private therapist for her son. Morgan said she has not returned to work because she has been unable to find a baby sitter. About 17 months ago, she and her husband, Robert, a building engineer, had a second son, Michael, who is normal.

Horowitz said the out-of-court agreement was reached last Friday and approved by D.C. Superior Court Judge Joseph M. Hannon. Horowitz said the settlement awards $400,000 to the parents, $200,000 to their son, and sets up a lifetime annuity for the child at $40,000 a year, plus 3 percent annual increases.