A dog responsible for inflicting bite wounds to the back of a 3-year-old girl's head has been killed, the Western Bay of Plenty District Council understands.

The toddler was flown to Tauranga Hospital from Matakana Island on Sunday after she was bitten. However, Western Bay of Plenty District Council is yet to receive any complaint.

Group manager of customer services Steve Hill said it had very little information other than what was already reported by the Bay of Plenty Times on Monday.

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.

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Mr Hill said the limited information made things "tricky" for the council in establishing what happened. ". . . we are investigating the matter," he said. "We have been advised that the dog has been put down but we haven't got evidence that that's the case."

Mr Hill said the council needed evidence about which dog was involved and who owned the dog before it could take action.