A comment was allegedly made about self-harming to security, so they contacted police who were trying to locate the pair when the tragedy unfolded.
NSW Police said in a statement on Saturday that they were not treating the incident as suspicious.
“Following extensive inquiries – and the availability of mobile phone and CCTV footage – investigators have established there are no suspicious circumstances,” NSW Police said.
“A report will be prepared for the information of the coroner.”
The incident caused the closure of two southbound lanes of the Harbour Bridge, and Harbour St was closed to southbound traffic.