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Members of the public said armed police gathered in the Mornington area after 5pm on Saturday in response to the incident.
The alleged offender gave himself up to police about 5.30pm, a police spokeswoman said.
A 23-year-old man has been charged with threatening to kill and possessing an offensive weapon. He is to appear in the Dunedin District Court on October 1.
The spokeswoman said police were called to a Hawthorn Ave property and the man had made threats against a person he knew.