A High Court jury has not been able to decide whether an Auckland man killed his baby son.

The Crown alleged the 32-year-old man, who has name suppression, assaulted his son while he was alone in the man's care and caused a massive brain bleed which killed him.

But the defence said the 11-month-old's death was "a dreadful and highly unusual accident" and the baby fell while he was out of the room, running a bath.

The jury deliberated at the High Court at Auckland for three days but were unable to decide whether the man was guilty of manslaughter.

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Justice Cheryl Gwyn discharged the jury this afternoon and thanked them for their service.

The man was supported in court by his wife and parents. He has been released on bail until his next court date next month.

During their deliberations, they asked to see the man's police interview twice and listen to his call to emergency services again.

After two days of deliberations, Justice Gwyn gave them a Papadopoulos direction, which is a direction to encourage jurors to persevere with their deliberations and to demonstrate a willingness, having listened carefully to the views of other jurors, to change their view.

Justice Gwyn also instructed them to consider a majority verdict whereby they were all agreed except for one juror.

'He's gone floppy'
The court heard how on December 7, 2017, the man was looking after his son alone and at about 7pm on the Friday evening went to run the baby's bath.

The defence said the man then heard a thud and went back into the living room to find his son crying and holding a pair of red headphones which had been on the couch. The baby had a thing for red at the time.

Defence counsel Rachael Reed, QC, said the man then put his son - he and his wife's first-born after numerous rounds of IVF - in a jumper where he could keep an eye on him from the bathroom.

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But when he looked back, his son's head was slumped to the side.

The court heard the man's call to Plunket, a number which he'd saved to his phone.

"I'm not sure what's happening with my boy ... He's gone completely floppy," he told the operator, starting to panic.

He told the operator he thought his son had fallen and was told to keep trying to rouse his son.

"Come on buddy. Come on buddy, come on. You're okay. Come on, wake up," he can be heard saying to his son.

"Oh my God, he's so stiff, he's so stiff."

Police spent a year investigating the baby's death and even bugged his and his wife's apartment, phones and car to try find evidence of a cover-up but didn't find anything.

During his interview with police about his baby's death - the day after his funeral - the man said he was confused as them about what had happened to their son.

"I don't understand what has happened," he told police.

"I want to find out what has happened more than you. He's my son and he's passed away and I want to know why."

He said his son was a lovely, smiley boy who was perfect in every way.

"I wouldn't hurt [him]. The thought wouldn't even cross my mind. He was not something that was easy to get as I've told you.

"We both wanted him. We both cared a lot for him."

During the trial, Crown prosecutor Henry Steele said the boy was either "a victim of an extremely rare accident or he was the victim of a fatal assault" - and those two possibilities were irreconcilable.

The Crown acknowledged the man was an attentive and loving father and that the baby was wanted and loved, he told the jury.

But something caused the man to snap, "to lose his rag" and assault his son, Steele said.

The incident happened at the end of the working week, after a bad sleep and during one of the few times he'd looked after his son alone.

"He's a good guy who did a bad thing."

The Crown said it was not reasonably possible for the boy to have fallen from in such a way to cause such a catastrophic injury, especially as he was still learning to stand. And the only evidence that the boy was able to pull himself up came from his maternal grandparents.

The only possible explanation for the boy's injuries was an assault by his father, Steele said.

A dreadful and highly unusual accident
But the defence counsel said the boy's death was "a dreadful and highly unusual accident".

And just because it was unlikely, didn't mean it was impossible, Reed said.

As well, the defence gave evidence the boy could have had a condition known as benign enlargement of subarachnoid spaces (BESS) because his head circumference was larger than his body.

BESS would have increased the baby's risk of injury, Reed told the jury in her closing statement.

There were also no other marks or injuries on the baby which would suggest he was the victim of abuse.

In fact, there were no red flags at all, the court heard.

During the trial several witnesses gave evidence and ran through the typical red flags. The baby had no historical injuries, the man was an attentive father, there was no history of family violence, no financial stresses or any reason for the man to hurt his son, the defence said.

Over the course of a year, police bugged the man's apartment and devices, sought search warrants and investigated the couple's finances to find evidence of the assault but they didn't find "a shred", Reed said.

And when weighed against all the evidence, it was inconceivable the man would hurt his son.