Teabridge Constabulary has increased patrols throughout the town following another death which detectives believe may be connected to the ongoing major investigation.
Police confirmed this week that investigators are examining similarities between the latest incident and two deaths reported last month.
No details concerning the victim have been released.
Officers have been visible throughout central Teabridge, with patrols concentrating around quieter streets, public footpaths and areas close to the river.
Chief Superintendent Evelyn Marsh said police understood that residents were becoming increasingly concerned.
“We are asking people to remain vigilant, particularly when travelling alone late at night,” she said.
Police have stopped short of advising residents to remain indoors and have stressed that there is currently no evidence suggesting attacks are random.
Several local businesses have nevertheless begun changing their opening hours.
The Willow Room Café has cancelled its Thursday evening opening, while The Flask & Fiddle has announced that staff will assist customers arranging taxis after closing.
For the first time, some residents have begun referring to the investigation as the “Teabridge Killings”.
Police have not adopted the term.