"I'm aware there are quite a lot of concerned residents across the Dunedin area who are worried about the incidents over the last week.
''I can't reiterate enough that we have an experienced and professional group of staff who are working extremely hard to resolve each of these cases.''
Insp Lloyd said talks of a ''crime spree'' are unfounded.
"While it is unusual for Dunedin to see this type of crime happening within a short period of time, it is key for the public to remember we have a very capable team of police staff who continuously work to keep our communities safe."
Detective Inspector Darryl Sweeney said police were making good progress in their investigations into the three incidents.
"Our staff are readily equipped to deal with these serious incidents," Det Insp Sweeney said.
"They've worked tirelessly over the last week to follow many lines of inquiry and continue to make progress in all three cases.''
However, police were still asking the public for help with each case, and Det Insp Sweeney urged anyone with any information to contact police.
Information case can be given by calling the Dunedin police station on 03 471 480003 471 4800.
Alternatively, information can be provided anonymously via the organisation Crimestoppers on 0800 555 1110800 555 111.