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Senior Sergeant Craig Dinnissen said police became aware of the incident at 2am.
A youth allegedly broke into St Vincent de Paul, in King Edward St, and stole the cash register.
An informant saw him smashing the register on Sutherland St before becoming "spooked" and fleeing.
The person was described as an "Asian teenager" with a short stocky build.
He was wearing a white cap, white hoody, dark pants and white gym shoes.
It is understood there was no cash in the register, which is now at the Dunedin police station, when it was stolen.
*An earlier version of this story incorrectly said the cash register was stolen from the George St St Vincent de Paul.