A Tauranga Hospital spokesman said the girl was discharged on Sunday but would not release any further information about her condition without the parents' approval.
Mr Hill said the limited information made things "tricky" for the council in establishing what happened.
"The hospital is not going to give us a lot of information . . . but we are investigating the matter. We are in early stages," he said.
"We have been advised that the dog has been put down but we haven't got evidence that that's the case.
"We are still in the throws of making contact with the family."
Mr Hill said the council needed evidence about which dog was involved and who owned the dog before it could take much action.
"There is no actual evidence that the family of the victim is involved."