The smile of the defendant was fixed this morning, as it often is when the testimony gets rough. Her chin was tilted defiantly upward. And although the detective on the witness stand was about to deliver what will probably be the most damaging police testimony against her, there was very little real emotion on Jean Harris' face as he told the jury of Harris' highly emotional outburst the night her lover was shot.

"She told me she had driven up from Virginia with the hope of being killed by Dr. Tarnower," the witness, detective Arthur Siciliano began, testifying for the prosecution in the Harris murder trial here. "She hesitated a second, then she said, 'He wanted to live, I wanted to die' -- she hesitated again -- then she said, 'I've been through so much hell with him . . . I loved him very much. . . . he slept with every woman he could, I'd had it."

The detective, a 30-year veteran of the force who talks with the accents of the New York City streets, paused here to use his hands.

"When she said 'I had it,' she made a gesture with her hands -- like pushing away," he said, "she also made an expresion. . . ."

An objection prevented the detective from showing what it was -- that would be expressing an opinion, defense attorney Joel Aurnou said.

Later, Siciliano spoke of a suicide note.

"She handed me a piece of paper," the detective said, "It had names of people to be notified in case her wish were completed. . . . . She also said she had no intention of going back to Virginia alive."

Former headmistress of the Madeira School in McLean, Va., Harris, 57, faces a sentence of 25 years to life on second-degree murder charges in the shooting death of her lover, Dr. Herman Tarnower. He died in the bedroom of his Harrison, N.Y., home last March.

The prosecution, noting that Tarnower had been seeing other women -- particularly his assistant, Lynne Tryforos, a woman 20 years Harris' junior, has maintained that Harris shot Tarnower "deliberately, consciously" in a jealous rage.

The defense argues that Tarnower's death was a "tragic accident," that Harris -- who went to the doctor's home with a bouquet of daisies as well as a pistol -- actually intended to commit suicide. She first wanted to say goodbye to the "human being she loved more than anything in the world."

Today's testimony, much of which was heard in pretrial hearings last month, lent some credence to the defense contention of suicide. It also supported their position that a struggle had taken place. But there was at least one moment, according to the police detective's account, when Harris remembered shooting the doctor.

"She says her and the doctor had a struggle," Siciliano said, telling the jury of his interview with Harris. ". . . . She said that she asked the doctor to kill her and he said, 'Get out of here, you're crazy,' and they struggled and that the gun went off several times . . . ."

The detective continued his testimony. "I asked her, 'Who had control of the gun?' She said, 'I don't know.' She said, 'I remember holding the gun and shooting him in the hand'. . . . Tears come in her eyes. . . . She got up off the chair, she asked me if she could see the doctor, she Said, 'Could I see Hy?' I said, 'I don't think that's a good idea.' As I recall, as it happened, that was the time they were bringing him [Tarnower] down . . . She puts her arms around me, and faints."

Earlier in the trail, the defense had seemed to make an attempt to establish that Harris was "not herself," that she was distraught, possibly operating under the influence of drugs. (Tarnower's housekeeper, testifying in court, had said that Harris, the night of the shooting, had seemed "very high.") The defense had also sought to establish, in extensive pretrial hearings, that Harris had never properly been read her rights -- the so-called Miranda warning, which gives a prisoner the right to remain silent.

On the stand for the second day to day, however, Siciliano, a man given to the technical turn of phrase of the long-time cop (a bedspread was described as being "five or six feet due east"), and an occasional disregard of grammar, said that Harris was aware of her situation that evening -- and she understood her legal position.

Repeating what he had said in pretrial hearings, Siciliano said that he had virtually forced Harris to listen to the Miranda warnings. He also said that Harris had declined medical attention for an injury apparently sustained during a struggle with the doctor, a slightly swollen lip.

"She said, 'I don't want no medical aid,'" testified Siciliano, ". . . She said, 'I had my rights read three times, you don't have to give them to me again. . . . '"

Neither, he testified, was Harris at any time incoherent.

"Any difficulty understanding what she was saying?" asked Assistant District Attorney George Bolen of his witness.

"None at all," said the detective.

"You had occasion to listen to her . . . observe her actions . . . do you have an opinion as to whether she was behaving in a rational or irrational manner?" Bolen continued.

"Rational," said the detective.

Cross-examination of Siciliano begins Tuesday.