Lindsay Clancy returned to court on Tuesday in her lawyers’ fight against a possible retrial after a jury earlier in September failed to reach a verdict on charges that she murdered her children – a proceeding that ended without definitive action.

Clancy’s team asked William F Sullivan, the superior court judge in Plymouth, Massachusetts, to deem Clancy, 36, not guilty of murder for killing her ⁠three young children in 2023, which she maintains she did while suffering postpartum psychosis and is therefore not legally responsible for. Sullivan on Tuesday only heard arguments on that request.

Meanwhile, the office of the Plymouth country district attorney, Timothy Cruz, again chose to not disclose whether it plans to try Clancy again.

Sullivan concluded the hour-long proceeding on Tuesday by setting another hearing on 2 November, when, he said, he wanted to discuss potential upcoming trial dates. A gag order requested by prosecutors against Clancy’s attorney, Kevin Reddington, is also expected to be considered at that hearing.

Sullivan held Tuesday’s hearing after declaring a mistrial on 4 September due to the deadlocked jury. A lone juror prevented the 12-member jury from agreeing to a unanimous verdict on whether to find Clancy guilty or not guilty by reason ⁠of insanity.

Several members of the jury have said 11 members of the panel wanted to find her not guilty by reason of insanity.

A first-degree murder charge carries a life sentence.

Clancy did not dispute at trial that she fatally strangled her children with ⁠exercise bands on 24 January 2023 in the family’s suburban Boston home. The former nurse then cut her neck and wrists with a knife and threw herself from her second-story bedroom window in an attempted suicide.

Reddington argued at trial that Clancy did not understand the wrongfulness of her actions and that she was experiencing postpartum ‌psychosis when she killed Cora, five; Dawson, three; and eight-month-old Callan.

On Tuesday, in a new posture, Reddington argued there was insufficient evidence to support beyond a reasonable doubt that she actually murdered her children or admitted doing so.

Investigators, he said, “just immediately assumed that this woman is guilty”, according to CBS News. “There’s no evidence that she admitted she did this … Why would she kill those three children?”

Redding also contended: “This entire case is based on speculation.”

Prosecutor Shanan Buckingham told Sullivan that this was the first time Reddington had questioned in court the sufficiency of the evidence linking Clancy to her children’s killings. Buckingham said the evidence of Clancy killing her children was “voluminous” and dismissed claims to the contrary as “laughable”.

Reddington said non-lawyers had difficulty understanding the notion that someone could admit culpability while also not being criminally responsible. He said that difficulty had prompted many public observers and high-profile figures to describe Clancy as a “demon” and demand her execution.

“This is coming from politicians,” said Reddington, who singled out Donald Trump.

When previously asked for his reaction to the verdict, the president said: “Look, she did a horrible, horrible thing. Can’t be worse. But you’ll find out what the price to pay is. There’ll be a price. It’s going to be mental institution or jail or something.”

If found not guilty by reason of insanity, Clancy would be committed to a Massachusetts state psychiatric hospital. The court would regularly re-evaluate whether to keep Clancy committed to that hospital.

Prosecutors don’t have to retry Clancy on first-degree murder charges. They could try brokering a plea deal or retrying her on second-degree murder charges, which would allow Clancy to waive a jury trial and be tried by a judge.

In arguing against a retrial, Clancy’s legal team has argued that jury notes clearly said the holdout juror had been ​refusing to apply Sullivan’s instructions on how to decide whether prosecutors proved their case beyond a reasonable doubt. Clancy’s attorneys contend that the holdout juror should have been dismissed rather ‌than allowing the case to ​be retried.

Her attorneys have also requested to review confidential records about the jury and question the holdout about his truthfulness during the jury selection process.

The holdout’s attorney, Edward Paltzik, has told Fox News that his client, Michael Desronvil, “had zero doubt” and “rigidly applied the reasonable doubt standard”.

In a video shared on Fox on Monday, Desronvil argued that focus on him should instead be channeled to “the ones that can’t defend themselves, and the ones that can’t fight the battles – and those are Cora, Dawson and Callan”.

The Associated Press and Reuters contributed reporting

In the US, the national maternal mental health hotline is 1-833-852-6262. In the UK, the Pandas foundation offers support via Whatsapp on 07903 508334. In Australia, the national maternal and perinatal mental health hotline is 1300 726 306