It is unclear whether congestion was a factor in Sunday's accident, in which a car is believed to have accelerated in reverse suddenly.
Road policing Senior Sergeant John Fagan said a woman's Honda vehicle had become stuck after its front wheels rolled over a kerb. Members of the public helped her push the car out.
As the car gained traction it sped backwards.
Police say the driver tried to brake but her jandal became wedged between the brake and accelerator pedals.
The car collided with the woman, and pinned her against another parked car. Police are investigating the crash and whether charges will be laid.
A Rurumoki St resident, who has lived in the street for 28 years, heard a scream and knew immediately what had happened. She rushed out and saw a woman on the road and called for an ambulance.
An off-duty nurse and paramedic were among the people first to help the woman before an ambulance arrived.
"It's a beautiful park and asset to Whangarei. Parking's out of control now with all the exercise groups and people coming to walk and run after work," the resident said.
Quite often she was unable to leave the property as people had parked cars on the footpath and on the grass berm in the middle of the road while attending fitness classes in the park.
Other residents were concerned that if there was an emergency that required a fire truck at a busy period at the park the appliance would be unable to reach them due to the number of cars parked on the edge of the road and footpath.
Whangarei District Council is not planning on adding more parking in the near future.
Group manager infrastructure and services, Simon Weston said there were no parking restrictions in the street, as long as there was adequate room to pass.
"The street has formal, designated carparks and is a designated slow street with a series of road humps to keep traffic speeds down.
"At the top of Rurumoki St there are a few formal carparks at the centre of the road," Mr Weston said.
The council permitted parking on the grass where it could be accessed, as long as it was safe and the parking did not cause excessive damage to the berm.
Mr Weston said businesses using the park for fitness classes did not need a permit to operate.
However, that was being reviewed.
