West Yorkshire Police appealed for information and arrested a 20-year-old man over the alleged assault in the early hours of Tuesday March 29 in the St Johns Centre car park.
The alleged victim was seen leaving Pryzm nightclub, in the Merrion Centre, Woodhouse Lane, at around 3.40am with a man.
Police say that after conducting “comprehensive enquiries”, detectives “are now satisfied that no offence took place and, as such, the investigation will be finalised”.
The man who was arrested was interviewed and later released without charge. Police say he will face no further action.
Detective Chief Inspector Mark Griffin, who heads Leeds District Safeguarding Unit, said: “We treat all reports of sexual offences very seriously and carry out comprehensive investigations to establish the full circumstances and gather all available evidence.
“The initial report of this incident was made in good faith and we have a clear duty to investigate such reports.
“As a result of our enquiries, we are now satisfied that no offence has occurred and therefore the man who was arrested after a public appeal has committed no crime.
“Social media has again proved to be a powerful tool in gaining the public’s help to assist our investigations.
“We would ask however that people now recognise the outcome of this investigation and consider the impact their continued comments can have.”