HOUSTON – Andrea Yates’s murder conviction for drowning her children in a bathtub was overturned by an appeals court yesterday because a psychiatrist for the prosecution gave erroneous testimony that suggested the Texas mother got the idea from an episode of “Law & Order.”

The ruling means Ms. Yates is entitled to a new trial, though prosecutors said they would try to have the conviction reinstated.

Ms. Yates, 40, is more than two years into a life sentence after a trial that stirred national debate over mothers who kill, postpartum depression, and the legal definition of insanity.

The appeals court ruling turned on the testimony of Dr. Park Dietz, a forensic psychiatrist who consulted for “Law & Order” and helped prosecutors land a conviction in 2002. Dr. Dietz testified at the trial that shortly before Ms. Yates’ crime occurred, “Law & Order” ran an episode about a woman who drowned her children and was found innocent by reason of insanity.

But it turned out that no such “Law & Order” episode existed.

“We conclude that there is a reasonable likelihood that Dr. Dietz’s false testimony could have affected the judgment of the jury,” a three-judge panel of the First Texas Court of Appeals said.

Calls to Dr. Dietz’s Newport Beach, Calif., office were not immediately returned. In its ruling, the appeals court noted that Dr. Dietz “acknowledged that he had made an error in his testimony.”

On June 20, 2001, Ms. Yates drowned her five children one by one, then called police to her Houston home and showed them the bodies of Noah, 7; John, 5; Paul, 3; Luke, 2; and 6-month-old Mary.

Ms. Yates pleaded insanity, and according to testimony at the trial, she was overwhelmed by motherhood, considered herself a bad mother, suffered from postpartum depression, had attempted suicide, and had been hospitalized for depression.

Five mental health experts for the defense testified that she did not know right from wrong or that she thought what she did was right.

Dr. Dietz, a nationally known authority who took part in the Jeffrey Dahmer and Unabomber cases, was the lone mental health expert to testify for the prosecution, and the only one to say she knew right from wrong. Ultimately, the jury rejected her claim of insanity.

“His testimony was critical to establish the state’s case,” the appeals court said. “Although the record does not show that Dr. Dietz intentionally lied in his testimony, his false testimony undoubtedly gave greater weight to his opinion.”

In his testimony, Dr. Dietz said he consulted for the popular NBC series and added: “As a matter of fact, there was a show of a woman with postpartum depression who drowned her children in the bathtub and was found insane and it was aired shortly before the crime occurred.”

Later, during closing arguments, a prosecutor referred to the Dr. Dietz testimony to suggest that Ms. Yates learned from the television show a way to escape responsibility for her actions. The prosecutor told the jury: “She watches ‘Law & Order’ regularly, she sees this program. There is a way out. She tells that to Dr. Dietz. A way out.”