Officers had appealed for information after it was alleged a 25-year-old was threatened with a weapon and sexually assaulted by another man on Brooms Road in the early hours of Sunday.
After checking CCTV and taking witness statements, police were "satisfied no criminality has taken place".
They said they were no longer looking for a suspect.
Det Insp Bryan Lee said: "I would like to thank the public for their excellent response to our appeals for information and reassure them they can go about their normal routine.
"Our additional patrols in the area will now also return to normal levels."

Surveillance camera footage showed people walking past the girl as she lay bleeding and unconscious.
It sparked a wave of condemnation and soul-searching on China's social networking sites.
Doctors had earlier said Wang Yue, who had been in a coma since the incident on 13 October, was unlikely to survive.
Anger and debate over toddler
Police have detained the drivers of both vehicles involved in the incident, which happened in the city of Foshan in southern Guangdong Province.
Wang Yue was knocked down by a van while wandering through a market, where her parents run a shop. The driver sped off without checking on the girl's condition.
Over the following minutes, 18 people walked past the bleeding toddler, and another van ran over her legs, but no-one stopped to help.
The distressing footage was shown on television.
A rubbish collector who finally moved the toddler to the side of the street was hailed as a national hero, but the incident led many online commentators to question the state of Chinese morality.
By Martin PatienceBBC News, Foshan
Other than the two chalk circles marked "1" and "2" on the road, there was little to suggest anything out of the ordinary.
The hardware stores selling irons, light fittings and taps were all open. Shopkeepers sat around chatting to each other.
But what happened on a covered street of this huge wholesale market last week shocked China.
A shopkeeper close to where the incident took place said she had been sickened when she saw the footage.
"Every time I watch it, my heart breaks," said Hu Haiou. "I catch the news every night to see if she'll survive. The people who walked by were shameful."
Another shopkeeper, Chen Guilin, said it had been raining hard the night of the incident.
"The raindrops sounded like drumbeats on the roof," she said, "We had no idea what happened outside."
Passers-by were 'shameful'
A spokesman for the hospital told the AFP news agency that Wang Yue had died of "systemic organ failure", adding that no expense had been spared to try to save the girl, whose parents are migrant workers.
There have been millions of internet comments about how to encourage good Samaritans - and many more expressing outrage that so many people refused to help.
Her death was one of the most remarked on topics on China's Weibo  - a micro-blogging site similar to Twitter - on Friday as people expressed sorrow and anger over the incident.
"Farewell to little Wang Yue. There are no cars in heaven," wrote one micro-blogger.
Guangdong province is debating the introduction of a law to force people to help others in obvious distress.
Initial online polls, though, suggest most people are against it.
"Talk about being civilised first. Is anyone paying attention to that?" read one posting.
Organisations in Guangdong are also looking at other ways to encourage people to act with compassion when faced with an emergency.
The provincial government's political and legal affairs committee is using its micro-blog site to gather opinions about how to "guide brave acts for just causes" and promote "socialist morals".
Several commentators have linked the failure of the passers-by to help with high-profile cases in which residents who stopped to assist people in distress were later held responsible for their plight.
Police investigating a report that a man was raped in Dumfries have now said no offence took place.
[NEXT_CONCEPT]
A two-year-old girl in southern China, who was run over by two vans and ignored by 18 passers-by, has died, hospital officials say.