Detectives launched an appeal for information after Graham Eddie, 42, (pictured) was found unconscious in his flat on Southcroft Walk on Saturday March 12.
Police said he had injuries to his face indicating he had been recently assaulted.
He was taken to hospital where doctors discovered he had underlying health issues. He remained in a life-threatening condition until his death on Tuesday March 22.
A South Yorkshire Police spokesman a post mortem was conducted on Thursday, adding: “The examination concluded that Graham’s facial injuries were minor and did not contribute to his death.”
The spokesman added: “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.
Anyone with information is asked to call police on 101, quoting incident number 743 of 12 March 2016.