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A police spokeswoman confirmed that police had attended the three incidents, reported when commercial staff arrived at work on Saturday morning, and "at this stage it is believed they are linked", she said.
The windows, one in the central city and the others in Andersons Bay Rd, were apparently damaged by some kind of small projectiles.
It is understood that a marble-like object was recovered after a pane of glass near the front door was damaged at the Dunedin branch of electrical supplier Redpaths in Cumberland St.
A pane of glass in the frontage at SGB Motors Ltd in Andersons Bay Rd was also damaged, in this case a hole being made in the glass.
Staff at the two businesses said the damage was discovered when they arrived to open up on Saturday morning, and police had been advised.
A third, apparently similar case - in which a window was shattered - was also reported to police on Saturday morning after staff arrived at a branch of Cooke Howlison Ltd, also in Andersons Bay Rd.
Asked if the damage could have been inflicted by someone travelling by car, a police spokeswoman said they would like to hear from anyone who had seen anything suspicious near the three buildings concerned.
Anyone with information can contact the police non-emergency number 105 or anonymously via Crimestoppers on 0800555-111