Last month, a 42-year-old North Carolina schizophrenia patient was discharged abruptly from St. Elizabeths Hospital while wearing a cotton dress, sneakers, a thin sweater and no underclothes.

She was told to go to a public shelter, but after walking the streets for six hours was readmitted. A day later, she was given a week's supply of medicine, bus fare, a list of shelters and was turned out again. Her discharge summary read: "destination unknown."

The woman's case was cited in a study released yesterday by three doctors at the Health Research Group to illustrate how the 1,200 homeless believed to be schizophrenic came to live in the streets, grates and public shelters in the District. The study found that nearly 40 percent of the city's homeless suffer from schizophrenia and that little is being done to aid them.

Federal officials said the figure is consistent with surveys nationwide that have found one-third to one-half of the homeless are mentally ill.

The study was based on interviews in January and February with the staff of 12 homeless shelters in the District. The staff members told researchers that schizophrenia was the main reason that 33 percent, or 441 of the 1,316 men in the shelters, were homeless. Alcoholism was the reason that another 40 percent, or 532 of the men, were homeless.

Officials at St. Elizabeths said the case of the woman cited in the study is under review and would not comment on it. "If the case is true, that's not good," said Dr. Shervert Frazier, director of the National Institute of Mental Health, which manages the hospital.

" . . . Homelessness is primarily the result of inappropriate deinstitutionalization," said the report's main author, Dr. E. Fuller Torrey, a former psychiatrist at St. Elizabeths Hospital, which is in the process of being transferred from federal to city control.

"This is the most psychiatrically rich city in the nation and the world," said Dr. Sidney E. Wolfe, director of the Health Research Group, and a coauthor of the report along with Dr. Eve Bargmann. "There are 1,300 psychiatrists, yet only two work in the shelters. There's only 25 hours a week available for all the needs of the homeless."

As a result of so many untreated mentally ill persons in the city's shelters, the facilities resemble "psychiatric wards of the 1930s" before medicines to help schizophrenics were created, the study found.

The report urges the city to require every psychiatrist to donate two hours a week as a condition of holding a license. It also asks that 15 psychiatrists at St. Elizabeths and 15 at the National Institute of Mental Health with administrative-only duties be asked to work in shelters part time.

"Given psychiatric manpower and monetary resources available in Washington, the existing mental health services for the city's mentally ill homeless are a disgrace . . . ," the report states.

Dr. Frazier said, "Most of our psychiatrists are heavily responsible for heavy expenditures of research money and are running the review committees." Forcing them to see patients "is not the way to solve the problem."

According to a 1984 National Institute of Mental Health study, the District spends at least twice as much as every state in the nation for mental health. According to figures supplied by the states for fiscal 1981, the District spent $151 per person for mental health, which was more than six times the average state spending of $24 per person.

" . . .If throwing money at a problem would solve it, then Washington would already be a model for public mental health services," the report said. It urged that money for St. Elizabeths be given to the District to follow the "mass exodus" of patients who left the federal hospital.

Mental illness was a larger problem for women, the study found, as 58 percent, or 210 of the 359 in shelters at the time, were schizophrenic. Alcoholism was the primary reason for homelessness among 14 percent of the women, or 50 cases.

The report was critical of the community mental health centers, which it said "have established records for unparalleled mediocrity."

Charles Siegel, a spokesman for the Department of Human Resources, which runs the city's community mental health centers, noted, "We have been improving our mental health system for some time, especially our Crisis Resolution Unit."