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Police have named the man found dead at a house in Williams Close in Gosport on Saturday, October 27.
He was David Michael Sharland, aged 48, of St. Vincent Road, Gosport.
An initial post-mortem examination was done but the results were inconclusive. Toxicology tests will be carried out on the body in due course.
The death is being treated as suspicious.
Two men, aged 40 and 43, from Gosport were arrested in relation to the death. They were questioned and bailed until December 20, 2012 pending further enquiries.
Detectives are looking into the possibility that all three men had been using drugs in the hours before the 48-year-old's death.
Officers have been examining the area, including nearby waste bins, for any evidence of drugs use.
There is no information to suggest a wider risk to the community.
Hampshire Constabulary would like to thank members of the public for their co-operation and assistance with enquiries so far.
Anyone with information is asked to contact the Operation Hillside team at Fratton Police Station by phoning 101. Mini-com users can phone 18001 101. Information can be given anonymously by phoning the independent Crimestoppers charity on 0800 555 111.