In his report released yesterday, coroner Richard McElrea said Staranise Waru was shaken to death by either her mother Nyree Hopa or father Robert Waru.
Staranise died in hospital in February 2006 from a severe brain injury.
Police launched a homicide investigation, but no one has been charged over the death.
Mr McElrea said that while he accepted the baby's mother wouldn't intentionally harm her child, he couldn't rule out that she shook the baby out of frustration.
He said he found the evidence given by the father unsatisfactory and that overall he was an unconvincing witness.
However, the exact identity of the perpetrator remained open as the necessary standard of proof had not been reached.
The officer in charge of the case, Detective Inspector Michael Johnson, said yesterday the findings confirmed the police view that one of the parents was responsible.
"The case currently is an open homicide investigation, which is in a holding pattern and in an inactive state until we can reassess it and see if there are any other investigative avenues we can explore," he told The Press.
He would not say what steps police might take or whether the parents would be re-interviewed.
"We are always keen to get to the truth of the matter and we would still love to be able to advance it and bring it to some closure for Staranise's family," he said.
