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Senior Sergeant Craig Dinnissen, of Dunedin, said the man was seen masturbating in Prospect Park mid-afternoon.
He was described as white, 1.73m (5 feet 8 inches) tall, with sandy-coloured hair, and facial hair.
A man matching that description had possibly been at the park the previous Sunday, Snr Sgt Dinnissen said.
"If anybody has seen anyone acting suspiciously in that area please call police.''