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Senior Sergent Craig Dinnissen said the man had gone to Countdown to purchase the eggs before heading to the nearby police station at 11.30am, to throw them at the front of the building.
The man was asked to cease his actions, but refused, demanding instead to be arrested.
The 55-year-old man got his wish and he was soon arrested for disorderly behavior.
Later that day, a man who had rear-ended a stationary vehicle at traffic lights along Princes St in Central Dunedin, sped through an intersection, only narrowly missing pedestrians.
The 41-year-old man was located shortly afterwards outside the Dunedin Central Night & Day, but refused to comply with breath testing procedures, Snr Sgt Dinnissen said.
Police arrested the man in relation to dangerous driving and refusing an officers request for blood specimen.