The Crown has accused the grandfather of the Kahui twins as being careless with the truth at an inquest into their deaths.
Three-month-old Chris and Cru Kahui died after being admitted to a children's hospital in Auckland in June 2006.
The boys' father, Chris Kahui, was acquitted of their murder following a High Court trial in 2008.
The twins' paternal grandfather Banjo Kahui on Thursday gave evidence at the Auckland inquest about what happened the night before the boys were admitted to Starship hospital.
Mr Kahui said after one of the twins briefly stopped breathing there was no discussion about taking that child to hospital.
At the earlier criminal trial, Mr Kahui had said there had been a discussion, but Chris Kahui decided against it as the baby had "come right".
When asked on Thursday if he had a habit of lying, Banjo Kahui answered: "I don't think so", to which Coroner Garry Evans responded: "I certainly hope not".
Police 'hindered by lack of information'
A senior police officer told the inquest on Thursday that there was nothing to alert officers to the possibility the babies were at risk.
Detective Superintendent Win van der Velde, the national crime manager, said that neither the twins' mother Macsyna King, nor Chris Kahui, had come to police attention for violence offences before the death of the boys.
On Wednesday the inquest was told that Child, Youth and Family was not informed that staff at Middlemore Hospital considered the babies to be at risk.
Mr van der Velde told the coroner a lack of information sharing is an impediment to preventing and investigating such cases.
He said since the boys' deaths, police have undertaken a number of initiatives to improve matters, including establishing a multi-agency centre in Counties Manukau which houses police child safety teams, social workers and district health board staff.
Mr van der Velde said police and Child, Youth and Family now compare databases on a monthly basis to identify high-risk families.
In the past year, the number of culpable child deaths had dropped from 17 to seven, he said.