North Yorkshire Police have issued a fresh appeal to help trace a laptop and bag belonging to Whitby murder victim Julie Davison.
Ms Davison was murdered on Wednesday 25 April in her flat.
Officers are asking anyone with information about her silver and black Toshiba laptop to contact them.
Detective Chief Inspector Steve Smith said: "Tracing the missing laptop and laptop bag is very important to the murder investigation and our desire to secure justice for Julie Davison and her loved ones."
Anyone with any information is asked to call Cleveland Police on 101.
Claire Montgomery has the latest from Teesside Crown Court.
James Allen appeared at Teesside Magistrate's Court charged with the murders of 81-year-old Colin Dunford in Middlesbrough and 50-year-old Julie Davison in Whitby. He also faced charges of rape, false imprisonment, assault and witness intimidation.
Allen smiled throughout the hearing and spoke only to confirm his name and address. When leaving the court he gave an obscene gesture to magistrates.
James Allen has been charged with the murders of Colin Dunford and Julie Davison. He has also been charged with rape, false imprisonment, assault and witness intimidation.
He will appear at Teesside Magistrate's Court this morning.
Detectives investigating the murders of Colin Dunford and Julie Davison have obtained a warrant of further detention for the 36-year-old man arrested in the Leeds area early yesterday morning.
James Allen is in police custody in Middlesbrough undergoing questioning in relation to the two murders and a sexual assault.
Police investigating the murder of Julie Davison are appealing for more information in connection with her death.
Officers are asking anyone who finds any discarded clothing or footwear in the Whitby or Scarborough area to contact them immediately.
They are also asking people to check their outbuildings and bins for signs of anyone living rough or any discarded personal items.**
Detective Chief Inspector Steve Smith, who is leading the investigation in North Yorkshire, said: "It is vital to our investigation that we piece together the suspect's movements over the past week.
" I am therefore reiterating the appeal for anyone who believes that have seen the suspect as he travelled across the region to contact us if they have not already done so."
Anyone with any information should contact Cleveland Police on 101 or Crimestoppers on 0800 555 111