West Midlands Police said a crime had taken place, but that new information showed it was not at the location initially reported.
The inquiry related to an incident reported to have happened in Sutton Coldfield’s Princess Alice Park on October 3 last year.
The force said that, following an investigation, it believed that the female who reported the matter knew her attacker and that the crime did not take place in the park but at an "undisclosed" location.
Meanwhile the victim had decided not to support an investigation regarding the new information.
Detective Superintendent Anastasia Miller, of the forces Public Protection Unit, said: “I want to thank everyone who helped our investigation by providing CCTV, checking dashcams and by speaking to us. I’d also like to thank Banners Gate Street Watch volunteers who helped us patrol the area.
“This was an exceptionally unusual case. The woman has now given us new information, but said that she does not feel able to support a continued investigation. We have taken our inquiries as far as we can and must respect her wishes. We have made it very clear that if she changes her mind, we will reopen the case with all of the information we have gathered so far.
“It’s important that people know just how seriously we treat reports of rape, and the care and support we give survivors. We listen without judgement and will always treat you with dignity and respect.”
The force said the female would continue to be supported.
Officers carried out door-to-door inquiries and checked street cameras to account for everyone going in and out of the park after the report was made, but detailed forensic analysis failed to provide any evidence.
The force said it was aware that residents were worried and some were even avoiding the park as a result. It said since the investigation was launched, improvements at the site included a request made to Birmingham City Council to prune overgrowth.
To report a rape phone 999 if immediate help is required. For non-recent attacks message via Live Chat.
If affected by rape help is available from The Survivors Trust on 08088 010818.