John W. Hinckley Jr., who was found not guilty by reason of insanity of attempting to assassinate President Reagan, was found semiconscious on the floor of his room at St. Elizabeths Hospital yesterday morning, apparently after taking an overdose of his own medication, a hospital spokesman said yesterday.

Hinckley, 27, who was described as blue from lack of oxygen and having difficulty breathing, was rushed by ambulance to the Greater Southeast Community Hospital, where he was being treated in the intensive care unit and was reported last night in serious but stable condition.

Wayne L. Pines, a spokesman for St. Elizabeths, said at a press conference yesterday that it was a "reasonable assumption" that Hinckley had attempted to commit suicide. Pines said late last night that "the prognosis is positive" for Hinckley to recover. He said complete lab results will be available later today.

Pines said that the hospital is investigating whether Hinckley may have saved up some of his medication and then taken an overdose yesterday.

Yesterday's incident apparently was the third time that Hinckley has tried to take his own life since he was arrested on March 30, 1981, outside the Washington Hilton Hotel and charged with shooting and wounding Reagan, presidential press secretary James Brady, a U.S. Secret Service officer and a now-retired D.C. police officer. Knowledgeable sources said yesterday that officials believe Hinckley may have taken an overdose of an anti-depressant drug that had been prescribed for him. Dr. James Levy, president of Greater Southeast Community Hospital, said at yesterday's press conference that officials suspect that Hinckley ingested "medication that he was taking" but he declined further comment.

Levy said of Hinckley, "We have every reason to believe he will be all right." He said Hinckley is on a respirator, to assist his breathing, and his stomach has been pumped. The U.S. Marshals Service has assumed security supervision of Hinckley while he is at Greater Southeast, law enforcement officials said. Meanwhile, Hinckley's apparent attempt to kill himself is being investigated both by St. Elizabeths and by Metropolitan Police.

Hinckley's chief defense lawyer, Vincent J. Fuller, said yesterday that he was "quite shocked" by his client's apparent attempt to kill himself. Fuller, who talked to Hinckley last week said, "He just seemed to be coping with his surroundings."

Hinckley's parents, who live in Evergreen, Colo., were informed of the incident yesterday.

After a lengthy trial in U.S. District Court last year, a jury found that Hinckley was legally insane when he shot Reagan and was not criminally responsible for his acts.

As a result, Hinckley immediately was committed to the John Howard Pavillion for the criminally insane at St. Elizabeths, where he will remain until he can prove that he is no longer mental ill and is not a danger to himself or others.

In May 1981, two months after he was arrested for the attack on Reagan, Hinckley took an overdose of the aspirin substitute Tylenol and the tranquilizer Valium while he was being held at the federal correctional institute at Butner, N.C. Officials said then that Hinckley had saved up the pills and then taken the overdose.

Six months later, Hinckley attempted to hang himself in his jail cell at the Army stockade at Fort Meade, Md. Hinckley, who used a jacket to form a makeshift noose, had jammed the lock to the cell door with cardboard to keep officials at bay and was unconscious when rescuers reached him. He was hospitalized but recovered with no permanent injury.

A St. Elizabeths hospital technician discovered Hinckley at 8:35 a.m. yesterday lying face up, clothed and semiconscious on the floor of his room on Ward 9 in the John Howard Pavillion, according to Pines.

A nightstand in the room was overturned, indicating Hinckley had fallen out of bed to the floor, Pines said, and there was vomit on the floor. Pines said that Hinckley had abrasions on his chin and knees that were consistent with a fall.

Pines said that Hinckley was having difficulty breathing and that the medical staff immediately administered oxygen and began cardio-pulmonary resuscitation. St. Elizabeths paramedics then rushed Hinckley to Greater Southeast Hospital by ambulance, Pines said.

Shortly after noon yesterday, Stephanie McNeill, a spokesman for Greater Southeast Hospital, said Hinckley's condition was "serious," meaning his vital signs, including blood pressure and heart rate, were irregular. McNeill said Hinckley had ingested some kind of "toxic" or poisonous substance and that he was "drifting in and out of consciousness."

During Hinckley's trial in federal court last year, defense psychiatrists testified that Hinckley suffered from a form of schizophrenia, a major psychiatric disorder characterized by a severe detachment from reality, delusions and deep depression. The psychiatrists testified--and Hinckley himself has maintained--that he attempted to kill Reagan to impress and prove his love for actress Jodie Foster.

During his trial, there was testimony that Hinckley had become obsessed with Foster, who played a child prostitute in the movie "Taxi Driver." Defense psychiatrists said that Hinckley saw himself in the role of the film's lead character, Travis Bickle, who stalked a presidential candidate. The film was shown on television in Washington Friday night, but Hinckley did not see it, according to knowledgeable sources.