Michael Ian Hancock, aged 43, was found dead in a flat in Badsley Moor Lane, Herringthorpe, in the early hours of Tuesday.
Two men, aged 19 and 23, and a 30-year-old woman, were arrested on suspicion of murder before being released as enquiries continue.
A post mortem examination proved inconclusive, with further tests now being carried out.
A South Yorkshire Police spokeswoman said: "At around 12.05am on Tuesday, emergency services were called to Badsley Moor Lane after the body of a man was found in a flat.
"A post-mortem examination carried out proved inconclusive and further tests are underway to determine the exact cause of Mr Hancock’s death.
"His family have been informed and continue to be supported by officers."