A nursing assistant stabbed to death on a cigarette break is thought to have been the victim of a "stranger attack".
Cheryl Moss was found stabbed in a nearby park
Police have no witnesses and no CCTV footage of the attack on Cheryl Moss, 33, behind St George's Hospital in Hornchurch, east London, on Thursday.
They think it unlikely Mrs Moss, from Dagenham, was attacked by a patient, as most are elderly.
"The chances are this person was hanging around for some time," said Det Supt Dick Langley.
He added: "Everyone assumes it's a man, but the reality is it... could be a woman."
So far detectives have found no CCTV footage of the attack itself but some items have been sent for forensics testing.
A man arrested over the death of Mrs Moss is likely to be released without charge, police said.
Because it was an apparently unprovoked attack and was outdoors Det Supt Langley said the investigation was likely to take some time.
He said they were not linking it to the murder of US artist Margaret Muller, who was stabbed to death in east London three years ago.
Mrs Moss had worked on the hospital's geriatric ward for more than a decade and was described as a popular and respected member of staff.
She had gone out for a cigarette break in a park behind the hospital on Thursday morning when she was repeatedly stabbed.
She was found at about 1100 BST and an ambulance was called but she was pronounced dead at the scene.
No murder weapon has been found and police said there was no evidence of a sexual attack.
Police have interviewed staff and are looking for witnesses
Security has been stepped up at the hospital to reassure staff, who are said to be deeply shocked.
Trainee nurse Imelda Distura, 34, said: "Everybody is upset... I am frightened really. We are asking for more security."
Mrs Moss's family visited the hospital on Friday to lay flowers and read tributes.
Their message, pinned to a bouquet, read: "Cheryl. Taken so cruelly from us. Will always be in our hearts. Dad and June."
Ralph McCormack, head of Havering Primary Care Trust, paid tribute to Mrs Moss, and said his thoughts were with her family, who have been too distressed to speak publicly.
"Cheryl dedicated herself to the support and care of others. She's been working in health services support for the last 17 years.
"She was very well respected and liked and known by her colleagues and had a great deal of admiration and respect from them.
"Clearly her loss will be a grave one."
The hospital is running most services as usual, although the nursery has closed for Friday and some staff who worked with Mrs Moss have not gone into work.