"We visited the centre, listened to staff concerns, looked at their policies, got expert opinion and then completed a public health risk assessment which concluded that there was no risk whatsoever."
The centre is run by He Puna Marama Trust, and CEO Raewyn Tipene welcomed Dr Jarman's findings, saying it brought some sense to the debate.
Mokopuna has been at the centre of a storm since the story broke last week, with the Aids Foundation criticising the centre for what it said was persecution of the boy.
But Ms Tipene said when the boy joined the centre his parents did not tell Mokopuna about his illness.
"If we had been informed when he came in February it wouldn't have been a problem and we could have done the risk assessment then and none of this [furore] would have happened."
"We would do that [risk assessment] for any child that comes with a pre-existing condition, so we could get a care plan in place, if needed, regardless of what that condition is.
"It's important that the right thing is done. It's not just about this particular boy, but about everybody at the centre, about keeping everybody safe."
Ms Tipene said parents should inform an early childhood centre if their child had any conditions or illnesses.
She said the fact it had taken Dr Jarman nine days to do the risk assessment showed it was not a simple matter.
She said the door was now open for the boy to return and Mokopuna would welcome him with open arms, but the boy's grandmother said he would not be returning to Mokopuna.
Dr Jarman said he felt the centre was well run and when he visited on May 9 it had policies in place that meant the risks for the transmission of any blood-borne virus were minimised.
One of the main recommendations from the public health risk assessment is that two Ministry of Health resources are used as reference documents for deciding on action plans for children with infectious diseases and that the Medical Officer of Health is consulted before any actions that could be perceived as exclusion because of an infectious disease.