The public have been told not to approach McKinnon if they see him.
He is described as white, 6ft and of slim build, with a shaved head. When last seen he was wearing a black jacket with a red hood, or red hood lining, and blue jeans.
The force said its enquiries had suggested McKinnon may have vital information in connection with the death.
Supt Craig Brady said: “We have a dedicated team of officers working to find Grant McKinnon. Our enquiries suggest he may have been in an agitated state when last seen.
“Officers remain in the area and searches are being carried out in a number of areas, which include specialist resources from our dog unit.
“We understand this police presence may be unsettling for the local community but please be assured we are doing everything we can to trace Grant.
“I am also appealing to the local community to assist us and asking anyone who knows where Grant is or where he might be to get in touch.”
