Ann Marie Farley (pictured), a former deputy manager of The Goose pub in Victoria Road, Aldershot, walked out of her bed-sit in nearby Elms Road at the beginning of December and was never seen again by friends.
Her partially clothed body was found in an unlocked shed by two boys aged six and seven who had wandered off from watching a football match off Wellesley Road in Aldershot on Sunday at about 1pm.
Detectives investigating her death are treating it as suspicious until post mortem results are completed today (Friday).
"We have to treat this as a murder inquiry until we know the cause of death," said Det Insp Alan Purvis.
Det Chief Insp Shirley Dinnell, who is leading the investigation, added: "We need to establish a picture of Ann Farley's movements from the time she left the bed-sit in early December until the time her body was found on Sunday.
"So far we have got very little information about where she was living during that period."
Mrs Farley had been living in the Elms Road bed-sit with three other people for about five months before she disappeared.
"Ann left the flat at the beginning of December and that was the last we saw of her," said Norman Richardson, who looks after the flat on behalf of landlord Malcolm Perry.
"We thought it was strange because she left all her property behind.
"We reported her missing to the police because it was so out of character.
"She said she was off to keep a doctor's appointment but I checked with the surgery and no appointment was ever made.
"After reporting her missing I heard nothing until Sunday when the police asked me to go to the station."
Speaking on Tuesday, Mr Richardson added: "We are all still in a state of shock because we only found out the body was Ann's last night. We are really devastated because we were all very close."
Mrs Farley was featured in the News last March at the official opening of The Goose pub where she was deputy manager.
But Mr Richardson said: "Ann was working at The Goose but lost her job and she was very depressed and upset about that.
"The mystery is that from the day we reported Ann missing to the day she was found she never returned to the house — she just walked out of the front door and totally disappeared.
"Ann was a really lovely girl and everyone liked her in the house. She had a heart of gold and we all thought a lot of her."
Police believe Mrs Farley had been dead for up to two days from when her body was found lying in a wooden trailer by seven-year-old Harri Jones from Guildford.
He alerted his grandfather Frank Jones, 57, of Waterloo Road, Aldershot, who called the police.
A major incident room has been set up at Aldershot under the codename Operation Wendover.
Anyone who knew where Mrs Farley went after leaving her bedsit in Elms Road can contact the major incident room at Aldershot on 0845 0454545.