"We're sorry for the obvious distress and pain this would have caused the girl during the incident and are pleased she is okay," he said. "However, had it not been for the actions of the man involved, officers would not have had to use pepper spray."
The spraying happened during a routine traffic stop. Police said Kira refused to give his details and tried to drive off.
The officer attempted to remove the keys but his arm was trapped when the man allegedly wound up the window.
"As the officer pulled his arm free, the window broke, causing minor cuts. Unfortunately during the arrest, a girl who was in the car with the man was accidentally contaminated by some of the spray.
"It is also sad that she is an innocent victim who has had to witness this incident, which could have been completely avoided."
A police spokesman said the man was now facing two charges of aggravated assault, and one charge each of failing to stop, and giving false details.
Amy was back home last night recovering.
A family spokesman said the incident had terrified the youngster.
The whanau disputed elements of the police version of events saying the officer took matters into his own hands and needed to be held to account.