The body of 43-year-old Paul Halley was discovered at 10.20am on Sunday, 29 July at a property in Hozier Street in the Carluke area.
Officers are treating his death as murder.
Forensics have been conducting enquiries and officers are continuing to carry out door-to-door enquiries, gathering private or public CCTV footage for review.
Detective Chief Inspector Raymond Brown, Major Investigations Team said: “We are in the process of trying to piece together Paul’s movements and to identify anyone he may have come into contact in the throughout Saturday until he was found in his home address on Sunday morning. We need to establish the exact circumstances of what led to his murder.
“Carluke is a close-knit community and local people will be concerned by what has happened. I would like to reassure them that we have a dedicated team of experienced detectives working on this inquiry, who are determined to find the person responsible for this crime. However, I require the support of the local community to assist us in our enquiries and provide any information which could be relevant to our investigation.
DCI Brown added that Mr Halley’s family have been left devastated following the death.
“Paul’s death has left his elderly parents, family and friends devastated and it’s vital we trace whoever is responsible”, he said.
“Anyone with information, regardless of how insignificant it may seem, or information as to who is responsible is urged to pass that information to police.”