Detective Superintendent Nick May from Surrey and Sussex Major Crime Team said: "We need to know the origins of this hammer.
"Do you recognise it? We need people to check if they have lost such a hammer or had one stolen in the period leading up to the murder.
"We would also ask police officers, prison staff, probation officers and professionals who work in mental health, if they have dealt with anyone who has talked about causing someone harm with a hammer, to let us know.
"If so we would like to hear from you. We are continuing to appeal for any information from anyone who saw anything suspicious in the area from late afternoon on Sunday 29 December to 10am on Monday 30 December to come forward."
Police have released these photos of a hammer which they believe is the weapon used to kill Valerie Graves in Bosham.
It was found in Bosham by the search team working on the murder inquiry.
Miss Graves was discovered dead in a ground-floor bedroom on the morning of Monday 30 December at the house in Smugglers Lane she was looking after with three other members of her family, while the owners were away.
She died from significant head and facial injuries.
The family of Valerie Graves who was found dead at a house in Smugglers Lane, Bosham, on Monday 30th December have paid tribute to her. Her family said: "Val was a much loved daughter, sister, mum and nan, who will be sorely missed by the whole family.
"Val was a free spirit who enjoyed her life and was a talented artist, about to embark on a new path involving ceramics.
"She was an eternal student, who was always hungry for a new challenge.
"She had recently moved back to Sussex from Scotland to be closer to her family and we were lucky enough to spend a family Christmas together.
"This has been a complete shock to the family and we appeal to anyone who has any information, no matter how trivial, to contact Sussex Police."
A woman who was found dead in West Sussex died from "significant head and facial injuries" according to a post mortem examination. Valerie Graves, who was 55, had been house sitting in the property on Smugglers Lane in Bosham when she was killed.
Police are continuing to appeal for witnesses to come forward.
The post mortem has revealed the cause of death but we are still keeping an open mind as to the motive. We are appealing for witnesses who may have seen anyone acting suspiciously or anything unusual in the area from late afternoon on Sunday 29 December to around 10am on Monday 30 December. Please call us if you know anything, no matter how insignificant you might think it is. It could be important to the investigation."