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The first of the two single-vehicle crashes happened about 3.15am when a vehicle travelling on Horse Gully Rd at Papakaio, inland from Oamaru, struck and killed a sheep that had wandered on to the road.
The driver was not injured.
The vehicle sustained significant damage to its front and was "likely to be written off", a police spokeswoman said.
About 90 minutes later a woman, believed to have fallen asleep at the wheel, veered off the road while driving in Arundel St in north Oamaru, the vehicle clipping a power pole and coming to a stop.
The 31-year-old from Oamaru, who was not injured, was issued with a court summons and is scheduled to appear in the Oamaru District Court on September 11 on a charge of careless driving.
In another incident on Thursday night, police received a report from a member of the public about 8.30pm that two people were "acting intoxicated" at Countdown Oamaru in Thames St, the spokeswoman said.
After the couple left the supermarket car park in a vehicle being driven without lights on, police observed it travelling on the wrong side of the road before it narrowly missed a group of pedestrians.
The 34-year-old female driver, of Oamaru, passed a breath-alcohol test but failed a roadside drug test.
She was issued a summons to appear in the Oamaru District Court on a charge of driving under the influence of a drug.