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.