Several witnesses were called to the stand who lived in or around Church Square in Whitby where the body of 50-year-old Julie Davison was found in her flat on the 25th of April 2012.
The prosecution alleges that James Allen travelled to Whitby after killing Colin Dunford in Middlesbrough.
The court heard from two witnesses who were in Julie Davison's block of flats in the hours before her body was discovered.
They say they spoke to a man they didn't recognise, who was sitting in the corridor of the ground floor.
Both said he had shown them his blood-stained sock, and told them that he had fallen off his bike.
The two witnesses then said that they had seen the man talking to a woman as they left, telling her she had to have her locks changed.
James Allen denies both murders and the trial continues.