"At this time police are not seeking anyone else in relation to Mr Neilson's death, however, the investigation remains ongoing and we believe there are still people in the community who may have information which can help," the statement read.
Anyone with information is urged to call police on 105.
Neilson's family have expressed their gratitude to the investigation team and the local community for their support through this difficult time, police said.
The circumstances of Neilson's death are yet to be released but police began treating it as a homicide from an early stage.
Police have said they are not in a position to reveal the results of that post mortem.