The authority found police units were not immediately available to respond to the emergency call. They also failed to give adequate priority to the incident.
Police also became suspicious that the child's injuries may have been caused by child abuse - but did not follow protocol requiring them to notify a child protection team.
Finally, police did not follow procedures on investigating incidents that occurred in one district, but were reported to police in another district.
The report revealed Auckland officers failed to record the complaint and include initial documents before sending the case to Counties Manukau.
Officers in Counties Manukau who received the complaint decided they did not have enough information and sent it back to Auckland. The authority found it was their responsibility to initiate follow-up inquiries.
Authority chair Judge Sir David Carruthers said it was crucial all police officers were open-minded to possibilities when a child was injured in unusual circumstances.
"Further, it is the responsibility of every police officer to have a good understanding of the internal procedures for reporting child safety concerns so that expert officers and other professionals can make a timely assessment.
"The immediate and ongoing safety of a child must always be the first priority. Consequently, it was unacceptable to presume that another officer would raise the flag."
The authority acknowledged this case was complicated as the incident and response took place across two police districts. "However, all officers working in the wider Auckland area should have a good understanding of established police protocols for dealing with cases across districts," Sir David said.
Police acting Assistant Commissioner Richard Chambers said police accepted they did not provide the child with adequate care.
"It is our responsibility to ensure that vulnerable children get the highest level of care and protection from police and we are disappointed that in this case we let the child, the family and ourselves down," he said.
Mr Chambers said police have put a number of measures in place to ensure these cases are managed efficiently.
"We are committed to ensuring that these sorts of incidents do not happen again and have already put a number of proactive measures in place to ensure that these matters are managed efficiently and effectively."
The measures included further training for Auckland police officers and to ensure they followed correct procedures with child protection reporting.
Counties-Manukau police have also accepted the findings relating to their handling of the complaint.
Mr Chambers said child protection issues were often complex and typically involved interaction with a range of various areas within police.
"This is why it is critical that we continue to communicate effectively across the organisation and with our agency partners so that we provide the best level of response we can for vulnerable children and families," he said.
Police acting Assistant Commissioner Richard Chambers said police accepted they did not provide the child with adequate care.
"It is our responsibility to ensure that vulnerable children get the highest level of care and protection from police and we are disappointed that in this case we let the child, the family and ourselves down," he said.
Mr Chambers said police have put a number of measures in place to ensure these cases are managed efficiently.
"We are committed to ensuring that these sorts of incidents do not happen again and have already put a number of proactive measures in place to ensure that these matters are managed efficiently and effectively."
The measures included further training for Auckland police officers and to ensure they followed correct procedures with child protection reporting.
Counties-Manukau police have also accepted the findings relating to their handling of the complaint.
Mr Chambers said child protection issues were often complex and typically involved interaction with a range of various areas within police.
"This is why it is critical that we continue to communicate effectively across the organisation and with our agency partners so that we provide the best level of response we can for vulnerable children and families," he said.
