Witnesses described hearing a woman scream, and it is believed a neighbour called emergency services after seeing her fall.
Police arrived a short time later but Mr Tostee had left the scene, the newspaper reported.
He handed himself in to detectives about 11am local time yesterday and was questioned for more than two hours at Surfers Paradise Police Station.
He was released without charge after being taken for forensic testing.
Regional Crime Coordinator Detective Superintendent David Hutchinson said police were treating the death as suspicious as a matter of procedure.
"In all cases like this - any sudden death which can't be explained - we treat as suspicious right from the start to ensure we determine what occurred," he told the Courier Mail.
Investigations into the circumstances surrounding the woman's death are ongoing, Queensland police said.
They have appealed for anyone with CCTV, camera or mobile phone footage of the area at the time Ms Wright fell to contact them.