Officers investigating took statements from hotel staff and an autopsy was conducted on Mr Kerry's body.
The first autopsy confirmed "there was no intervention" to the outside of Mr Kerry's body, police added.
A final autopsy result is expected in two months' time.
The lift had been out of use, according to police, and there was "no proof of firearm or sharp object injuries".
Mr Kerry had been visiting Turkey along with his girlfriend Molly, his grandparents and other relatives on 27 November.
They had been enjoying a drink at the hotel bar in the early hours of 29 November when Mr Kerry, who had fallen asleep on a sofa, vanished.
Mr Read said he found his brother, who was a labourer, at the bottom of the lift shaft in the hotel basement during a panicked search.
"My brother's been killed, 100%," Mr Read previously said. "I want to see justice for my boy.
"It's killing me sitting here thinking of everything that could've happened to him.
"Me and the family, we can't cope just living in the dark. We need to know now."
The family previously said he was found "flat on his face" with just a pair of boxers and socks on.
A spokesperson for the hotel said staff had been supporting the family, but were unable to comment further due to the police investigation.