Testing with a sound hammer did not highlight any acoustic anomalies, indicating that decay identified on its surface were localised and superficial.
Park director Michael Ayrton said all mature trees were assessed each year.
"We were deeply shocked by this fall, and well aware how traumatic it would have been for the people affected, and we are very grateful at it did not cause serious physical injury," he said.
The park was commissioning a peer review of tree health processes to see if any changes were needed.
Trees that did not meet the assessment criteria would continue to be removed.
West Auckland woman Dallas Hargreaves, 72, was trapped when the cottonwood unexpectedly crashed to the ground over four parked cars.
She was dragged from her mangled vehicle by off-duty police officer Sergeant Adrian Heffernan and treated for leg injuries in hospital.