The jury in the Lindsay Clancy trial has been allowed to go home and will now continue its deliberations on Wednesday after earlier admitting it was unable to come to a unanimous decision in the case of the mother who killed her three children.

Judge William Sullivan released the jury with the deliberation clock on 23 hours.

"My understanding is that you requested to be excused until tomorrow at 9 o'clock," the judge said. "I just want to thank you for your hard work and commitment."

Sullivan instructed jurors not to read, listen or talk about the case until their deliberations resumed.

In the first sign that jurors were struggling to reach a verdict they had sent a note to the court saying they were deadlocked. But Sullivan told the jurors that he understood it had been a long and complex trial and sent them back to continue their talks.

"I'm going to ask you to go back out," he said.

Clancy, a former labor and delivery nurse in Massachusetts, does not deny strangling her children but says postpartum psychosis led to her actions. Prosecutors argue she knew what she was doing. Clancy, 36, has pleaded not guilty by reason of lack of criminal responsibility.

The jury could convict her of murder or manslaughter, or acquit her if jurors believe her deteriorating mental health was to blame. A conviction could lead to a life prison sentence. If she is acquitted, a judge could still order her confined to a mental health facility if an evaluation determines she is a danger to the public.

Tuesday marked the fourth day of jury deliberations, which began after closing arguments on Thursday.

Clancy's lawyer argued at the trial that she loved her children, but killed them because she had lost her grip on reality – and on herself – due to postpartum psychosis, a rare mental illness that can follow childbirth. In the months before the killings, Clancy sought treatment for her worsening mental health, including a stay in a psychiatric hospital.

To be found guilty, Massachusetts law requires defendants to retain "the substantial capacity to appreciate the wrongfulness or criminality of their conduct and to conform their conduct to the requirements of the law".

Patrick Clancy, Lindsay's former husband, was among those to testify during the trial, in addition to relatives, psychologists and physicians who treated her. Jurors learned that Clancy had been prescribed 13 different sleep and anxiety medications, with her attorneys maintaining that may have exacerbated her depression symptoms.

After Clancy's criminal trial, the focus is going to shift to civil litigation brought by both Lindsay and Patrick against her medical and mental healthcare providers. The former couple accused the providers of medical malpractice, contending they failed to properly diagnose, treat and monitor her severe postpartum psychiatric condition.