Devinder Sivia, an Indian-origin Mathematics lecturer arrested in connection with the death of his colleague in Oxfordshire, was on Friday released on bail until April 18, the police said.
The incident has shocked the academic community in Oxford. Sivia, 49, and victim Professor Steven Rawlings, 50, were described as close friends for decades who had even co-written a book.
Rawling's body was found in Sivia's house in Southmoor, Oxfordshire.
The Thames Valley Police said a post-mortem examination carried out has proved inconclusive and further tests will be undertaken over the forthcoming weeks.
There is no charge against the Indian-origin lecturer Sivia.
Linda Davey, 64, Rawling's older sister, told The Telegraph that he was not the type of man to get into an argument over anything.
She said, "They have been friends for 30 years. We can't think that there was any kind of fight. We can only assume that it was a terrible accident. Steven was big, but he was gentle."
Vice Chancellor of Oxford University Professor Andrew Hamilton said, "The entire University community has been profoundly saddened and shocked by the tragic and untimely death of Professor Steve Rawlings. Our thoughts are with his family and friends."
Detective Superintendent Rob Mason said, "This is a tragic incident and our investigations are going on to establish the cause of death. A substantial amount of information is already in the public domain and we can confirm that the two individuals involved have been friends for over thirty years".
Sivia, who is a stipendiary lecturer in Mathematics for Sciences at Oxford University, lectures to undergraduates studying chemistry and physics and has published two books.
Local resident Duncan Logan, who lives opposite the house of Sivia, said he had known both academics for several years and described them as "the best of friends".
He said, "I can't believe what I am hearing, it is like a bolt from the blue. They were the best of friends. They were nice, gentle, well-spoken, polite and hard working people. I am proud to have had both of them as friends. I never heard them fight."
He added, "They seemed to respect each other enormously, and talked very highly of each other. I got a text about it today and at first I thought it was Devinder who was dead. I can't imagine Devinder hurting anyone. I have never even heard him raise his voice. He is such a gentle person".