The mother of a five-month-old who was allegedly murdered has given tearful testimony recounting the day of the girl's death.

Troy Louis Stuart Solomon, 25, is on trial before the High Court at Auckland charged with the murder of his daughter Aaliyah Izabella Betty Solomon.

Solomon initially told police the baby had drowned in the bath but later changed his story saying he had dropped the girl when lifting her out.

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Man accused of killing baby claims he accidentally dropped her

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Crown prosecutor Aaron Perkins dismissed both explanations as "utter nonsense".

He said Aaliyah had "catastrophic head injuries" and a broken left femur, which were consistent with her being swung around before her skull abruptly met a hard surface.

The baby's mother, whose name is suppressed, told the court she and Solomon were still in a relationship despite the allegation he had murdered their child.

She said on the morning of August 7, 2014, she had walked to the supermarket, leaving the defendant at home with their daughter.

Aaliyah had had her bottle and the witness tearfully recalled cuddling her before she left.

The woman then described walking home from the shops and hearing sirens before getting a call from Solomon, who was screaming at her to return.

"I had the phone away from my ear because he was yelling. I just started running home," she said.

"The police stopped me going in, but I could see baby. Everybody could."

She said she spent the night in a car with her partner and quizzed him about what had happened.

"He wasn't really saying much. He was more upset because he failed at protecting the baby, that's what he said to me," she told the jury.

When police arrived at the scene, the defendant told them he had been briefly preoccupied before returning to find his daughter underwater in a baby bath.

The following day though, armed with information from the pathologist about the victim's injuries, police took the man to the station for further questioning.

Mr Perkins said Solomon "steadfastly maintained" his account that Aaliyah had drowned.

But later the 25-year-old asked to return to the interview room where he then told police for the first time that he had dropped the baby accidentally.

Solomon said he was stoned from smoking cannabis and had not told the truth beforehand because he was "too much of a drop nuts".

"The Crown position is his explanation is utter nonsense," Mr Perkins said.

"Mr Solomon knew the drowning story wasn't going to work... he had to change his story and give some account for the injuries that had been discovered by the pathologist."

But the prosecutor said his version of events would be rubbished by medical experts called to give evidence.

The break to the baby's femur was a spiral fracture, which Mr Perkins said could only be caused by a twisting motion.

Defence lawyer Phil Hamlin said his client accepted responsibility for his daughter's death but "that did not amount to murder".

"There's no way he intended in any shape or form to harm her or to recklessly kill her, as the Crown case relies upon," he said.

"What happened was a terrible accident. It's a tragedy he continues to feel right through to this day."

The trial before Justice Paul Davison and a jury of nine women and three men is scheduled to run for three weeks.