Senior Sergeant Anthony Bond, of Dunedin, said police spoke to a youth who was "a person of interest" as the source of the threat which sparked the armed response.
The investigation was ongoing but no one else was being sought over the matter.
On Tuesday, Bayfield High School went into lockdown following a threat sent by email at 8.45am before the NCEA level 1 science axam and level 2 chemistry exam.
Armed officers were stationed at every entrance to the school and warnings were played over loudspeakers.
Concerned parents were gathered outside the police cordons around the schoopl as pupils were kept under lockdown until about 10.30am.
A police spokeswoman said they needed to take threats seriously until they had evidence to prove otherwise.
‘‘Officers subsequently confirmed that there was no risk to staff or students.’’
