One of the officers then used his pepper spray on the man and he was pulled out of the car and handcuffed.
The child's mother complained to the authority that police had deliberately sprayed the three of them.
The authority accepted that the 10-year-old girl was badly affected by the pepper spray, but found the officer did not deliberately spray her or the woman.
Authority chairman Judge Sir David Carruthers said the use of pepper spray in the situation had not been carefully considered.
"There is no doubt that this was a dynamic situation. However, when spraying the man, the officer did not properly consider the necessity of using pepper spray in a confined space, the likelihood that it would affect the other innocent passengers or the fact that he was using a more powerful spray."
Although the authority was ready to release its report in September this year, ongoing court proceedings prevented it from doing so.
Whakatane Area Commander Inspector Kevin Taylor said police apologised for the "unnecessary distress and pain this caused [the girl]".
"She also had to witness an incident that could have been completely avoided if the driver had complied with his legal requirement to provide his details.
"What should have been a routine traffic stop quickly degenerated into a volatile scenario.
"In situations like these, events unfold rapidly and decisions need to be made quickly.
"Our officers responded to the situation confronting them to protect themselves and keep the community safe."