David Stead, aged 32, was found seriously injured at the house in Harold Grove, Hyde Park, in the early hours of Tuesday, May 8.
He was given emergency treatment by paramedics but was pronounced dead at the scene.
His death is currently being treated as unexplained.
A 25-year-old man who was arrested on Wednesday in connection with his death remains in custody on a warrant of further detention.
A 39-year-old man who was arrested has been released without charge.
Detectives are now appealing for information to help build up a picture of movements in the time leading up to his death.
He was last seen leaving the Sainsbury’s store, in Royal Park Road, Hyde Park, at 10.43pm on Monday, May 7.
Detective Chief Inspector Chris Gibson, of West Yorkshire Police Homicide and Major Enquiry Team, said: “We are currently treating David’s death as unexplained and are continuing to carry out enquiries into the circumstances.
“We are working to build up a picture of his movements in the time leading up to when he was found seriously injured at his home, and we are keen to hear from anyone who has seen him at any point between when he left the Sainsbury’s store in Royal Park Road on Monday night and when he was found at his home in Harold Grove in the early hours of Tuesday.
“The CCTV image shows how he was dressed in a distinctive light-coloured Adidas t-shirt with the logo on the front.
“I would like to hear from anyone who has seen him during that period or who has any information that could assist the investigation.
“David’s family are absolutely devastated at his sudden and unexpected death and we are supporting them at what is clearly a very difficult time.”
Anyone with any information that could assist the investigation is asked to contact 101 quoting Operation Panelshot or online via https://www.westyorkshire.police.uk/contact-us .
People can also call the independent charity Crimestoppers anonymously on 0800 555 111.