Graham Eddie, aged 42, was found in his flat by a friend at Southcroft Walk near Abbeydale Road on the morning of March 12.
A post-mortem examination conducted yesterday evening found that Mr Eddie had underlying health conditions.
A South Yorkshire Police spokesman said: “The examination concluded that Graham’s facial injuries were minor and did not contribute to his death.
“Graham was discovered by a friend on Saturday 12 March in the morning, in his flat in Southcroft Walk. He was unconscious and had facial injuries including swelling and cuts.
“He was taken to hospital where it was discovered he had underlying health conditions. He remained in a life-threatening condition until his death earlier this week.
“Officers remain keen to hear from anyone who may have seen Graham in the days leading up to his death.
“A 50-year-old woman was arrested on suspicion of assault as part of the investigation. She has now been released without charge.
“If you have any information that could help officers, please call 101 quoting incident number 743 of 12 March 2016. You can also give information to Crimestoppers anonymously on 0800 555 111.”