The 62-year-old man who was murdered at a house in Magherafelt was Brian Coulter.
His body was found at a house in Sandy Braes just after 12.30pm on Monday (18 October).
Detective Chief Inspector Raymond Phelan said a man was arrested nearby on suspicion of murder.
“I am asking for help from the public to identify sightings and movements of Brian since last Monday, 11 October. I am particularly keen to hear from anyone who saw Brian, together with descriptions of anyone who was in his company through to Monday 18 October.
“If you have any information which you think could help, please contact detectives on 101 quoting reference 944 of 18/10/21,” he said.
A report can be made using the online reporting form via www.psni.police.uk/makeareport. Information can also be provided to Crimestoppers anonymously on 0800 555 111 or online at www.crimestoppers-uk.org.