The body of Carl Scott, 37, was found by a member of the public at a property in Birch Court in the Stanmore area on Wednesday afternoon.
Police said a 58-year-old man from the city has been bailed until 7 June.
Detectives have appealed for information from anyone who had recently been in contact with Mr Scott.
A man arrested on suspicion of murder following the discovery of a body at a house in Winchester, has been released on police bail