The denim shirt was reported to police by a member of the public just after noon on Friday.
It was discarded among trees outside the Dunedin Railway Station and may have been there overnight.
Police are investigating three serious incidents against women in Dunedin last week after 51-year-old Dunedin woman Karin Ann Ross was found dead in the car park of the cleaning company where she worked, a 23-year-old jogger was tied up and sexually assaulted in the Ross Creek Reserve and a 45-year-old cyclist was attacked in Portsmouth Dr.
The Otago Daily Times understands police believe foul play was involved in the death of Ms Ross.
A police spokesman confirmed yesterday they were investigating whether the shirt was linked to any of the incidents.
"Police are making inquiries into where the shirt came from and what potential links there may be to any ongoing investigation,'' he said.
The shirt is being forensically examined and investigators are awaiting those results.
Police have moved to reassure Dunedin residents following the violent crimes.
Acting Otago Coastal area commander Inspector Kelvin Lloyd said the incidents were not linked.
"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,'' he said.
"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.
"I can confirm these cases are in no way linked to each other. For operational reasons, and while a homicide investigation is ongoing, I'm not in a position to explain in detail why they're not linked, but the information police currently have strongly indicates this is the case.''
Talk of a crime spree gripping Dunedin was "unfounded'', he said.
Detective Inspector Darryl Sweeney, who has oversight of the three investigations, said police were making progress in the three cases.
The scene investigation of a Nairn St address owned by a co-worker of Ms Ross continued yesterday, but police remained tight-lipped about their inquiries.
A security guard remained at the scene and unmarked police cars were outside yesterday afternoon.
It is understood police are examining several vehicles in relation to the death.
Det Insp Sweeney would not comment on the nature of Ms Ross' death or the injuries she suffered.
Her co-workers returned to work yesterday and there was no visible police presence at the business.
A Spotless spokeswoman said staff were offered counselling.
