Part of the damaged mudguard rubbed on the tyre when she tried to drive the car, so she had to get her great-nephew to remove it completely.
Smith phoned her insurer to describe what had happened and to ask about repairs.
Then she called the police, who said there was nothing they could do. But they recommended she contact the Waitaki District Council's animal control department.
"I am sure there were at least two dogs and one of them sounded large with a deep bark and another a smaller dog with a lighter bark," she said.
"Both sounded quite frenzied.
"I feel that if dogs are roaming the streets at night and can inflict such damage on a car, what can they do to an unwary human?"
She was also concerned about the penguins that came ashore nearby.
Smith wondered if the stray cat had climbed on to her car tyre to try to escape the dogs, to no avail.
Her sister recognised the dead cat as one of a group of neighbourhood strays.
Council regulatory manager Andrew Bardsley said he spoke to Smith and assured her he would follow up on the matter.
The council has asked its animal control officers to carry out evening patrols around the area.
It also reminded residents to make sure their dogs could not roam at nights and did not pose a danger to people or animals.