The 23-year-old assistant of artist David Hockney did not die of "obvious" natural causes, a post-mortem has revealed.
Humberside Police said that results from the post-mortem showed there were "no obvious natural causes" for the death.
Further toxicology tests could take between six and eight weeks, police said. Detectives had previously ruled out violence as a factor in Elliott's death.
Officers will continue to investigate how Elliott became ill before being rushed to Scarborough Hospital, reportedly by Hockney's partner, John Fitzherbert. It is not known if the 75-year-old painter was home when Elliott was taken ill.
It is believed that Elliott had failed to turn up for a rugby game the day before his death. His team-mates said that his no-show was unlike him.
It is reported that the 23-year-old had been drinking heavily the night before his death.
Humberside Police said: "Mr Elliott's family has been fully updated by Humberside Police."
Bradford-born Hockney, who painted a picture of Elliott in 2008, is considered one of Britain's leading living artists. More than 600,000 people visited his show, A Bigger Picture, at the Royal Academy in 2012.
His 1963 painting, Great Pyramid at Giza with Broken Head from Thebes, was recently valued at £3m by auction house Christie's.