The woman found dead in a shed on Army land last Sunday has been identified as Ann Marie Farley (42), who lived in a bed-sit at Elms Road, Aldershot, until early December.
Murder squad detectives are still trying to establish exactly what caused her death.
Contrary to earlier reports, Detective Inspector Alan Purvis said on Monday that so far they had found no evidence that the victim had been strangled.
He told a press conference at the scene: "We are treating this as a murder inquiry, but there is no obvious cause of death.
"Pathology tests are being carried out and we hope to know the results by Friday at the latest."
Det Chief Insp Shirley Dinnell, who is leading the investigation, appealed for anyone with information about Ann Farley to contact the incident room at Aldershot on 0845 45 45. The inquiry is codenamed Operation Wendover.
"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, Jan 13.
"In particular, we need to know where she was living during that period," Det Ch Insp Dinnell said.
Anyone who knew Ann Farley is asked to contact the police, who promise that officers will treat all information with discretion.
Ann Farley's body was found by two boys, aged six and seven, at a sports field alongside the main A325 road at Aldershot.
They made the macabre discovery after wandering away from a football match, which they were watching with their grandfather.
The youngsters went into a groundsman's corrugated iron shed and saw the body lying on a trailer.
Police cordoned off the area and the body was moved to the North Hampshire Hospital at Basingstoke.
Home Office pathologist Dr Nicholas Hunt conducted a post mortem on Sunday night. He concluded that the body had been in the shed for between 36 and 48 hours.
Soon after the discovery officers carried out a detailed search of the area surrounding the shed, much of which is covered in bracken.
The Ministry of Defence sports field, which is entered from Wellesley Road, off Bourley Road, is popular with dog walkers.
And police are appealing for anyone who saw people around or entering the shed between January 5 and 13 to contact them on 0845 045 45 45.
Ann Farley is described as white, 5ft 2in to 5ft 3in tall and of fairly heavy build. She is understood to have been wearing a jumper and jeans.
Police were unable to say on Monday if she was married.
About 25 officers are involved in the inquiry. They are being assisted by Ministry of Defence police.