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Southern District crime services manager Detective Inspector Steve McGregor said the girl was mistaken for Madeleine on New Year's Eve, in Queenstown.
Scotland Yard had advised police a DNA sample voluntarily taken from the girl was showed she was not Madeleine.
The DNA test result, as requested by Operation Grange - the British police operation investigating Madeleine's disappearance - supported and confirmed the original New Zealand police investigation's conclusion, he said.
The girl's family said although they appreciated the concerns raised by the public, they wished to maintain their privacy.