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Joan Wilson was driving a 2016 Hyundai Santa Fe when she crashed near Roxburgh in late December.
Documents obtained under the Local Government Official Information and Meetings Act (LGOIMA) by blog "What if? Dunedin" reveal the $55,659 vehicle had been in use for just five days before the crash.
In a statement to the Otago Daily Times Mr Cull said his wife sustained "serious injuries" in the crash.
"Joan was the sole occupant in the vehicle.
"Fortunately, she is making a gradual recovery and I would like to take this opportunity to thank the emergency services and members of the public who provided assistance at the scene," Mr Cull said.
The accident was a "private matter" and no further comment would be made, Mr Cull said.
Dunedin City Council strategy and governance manager Sandy Graham said the Mayor paid for full private use of the mayoral vehicle, and the vehicle was able to be driven by any authorised driver.
Mrs Wilson was an authorised driver.
Insurers had not identified the cause of the accident, and no other vehicles were involved.
The council received a full insurance pay out of $53,043 (excluding GST) and a replacement 2017 Hyundai Santa Fe was bought for about $56,000 in March.
The former mayoral vehicle, a 2011 Peugeot 508 GT, bought in 2011 for about $60,000, was used while the replacement was found, LGOIMA documents showed.