The deceased body of Maria Rawlings, aged 45, was found in shrubbery in the Little Heath area of Essex.
Cause of death is said to be "neck compression and possible blunt force head trauma".
Maria Jane Rawlings: Mum found dead near hospital was murdered
Detectives say Maria Jane Rawlings attended King George's Hospital, in Ilford, on 3 May and left on foot in the direction of the A12.
They believe the 45-year-old, from Chelmsford, Essex, was approached by someone while walking on Barley Lane.
Her body was found at about 14:00 BST the following day in Little Heath.
Cause of death is said to be "neck compression and possible blunt force head trauma".
Maria Jane Rawlings: Mum found dead near hospital was murdered