The Supreme Court heard arguments yesterday about whether the University of Missouri School of Medicine in Kansas City violated the constitutional rights of Charlotte Horowitz when it expelled her shortly before graduation in 1973.

Horowitz, who lives in northwest Washington, has been unemployed for four years, blaming the "stigma" of expulsion. She had been promised a research jon on condition that she get her M.D. degree.

Her intellectual brilliance, demonstrated by course grades and a variety of tests, was not at issue. Marvin E. Wright, lawyer for the university, acknowledged it at the outset of his argument.

He emphasized, however, that the school also required students to demonstrate that they could practice medicine. He said the school expelled Horowitz because she failed in this regard through repeated failures of personal hygiene, such as unkempt hair, dirty fingernails, and wearing of dirty or yellowed lab coats, and an inability to get along with physicians, patients and fellow students.

Horowitz, now in her 30s, was among the spectators, wearing a neat plaid suit. Her black-and-gray hair was neatly arranged. She told reporters she had no comment.

Her lawyer, Arthur A. Benson II, argued that the school had deprived her of her rights - principally the right to get a job in the medical field and to get a medical degree anywhere - by expelling her without giving her adequate notice of the charges against her and by not giving her a hearing. That, in essence, was the holding of the Eighth U.S. Circuit Court of Appeals in July, 1976.

Benson drew a volley of questions that were at least implicitly critical of his and the appeals court's position.

Justice John Paul Stevens asked the Kansas City lawyer to identify the "principal procedural defect" in the school's months-long process that culminated in the expulsion.

Benson said the defect was a denial of due process: the school did not let her appear before a committee that dismissed her, although she had met individually with each of seven physicians on a panel of outside advisers who had made a recommendation to the committee.

Justice Stevens asked for a legal precedent that an individual who had appeared before a panel empowered to make a recommendation had a right to a hearing before a committee empowered to make a final decision.

Benson could offer no precedent that was precisely on point. The justice told him, "This is your critical argument and you have no case to back it up."

Justice William H. Rehnquist suggested that an expulsion from medical school "foreclosed fewer opportunities" for a job than being flunked from college or even high school.

His implication was that a ruling for Horowitz might extend widely, so that all publicly financed educational institutions would have to provide notice of charges and an opportunity for hearing before expelling a student.

Benson replied that requiring a due process hearing - a more elaborate one for higher than for lower education - "would not place any undue burdens on the institutions."

University attorney Wright, of Columbia, Mo., argued that because the school had advised Horowitz that she was in difficulty long before expelling her, she had been on notice.

The expulsion "did not come as a bolt of lightning from the sky," he said. She assumed she could earn her degree "by reading books instead of treating the patients," he added.