The X Factor judge was voluntarily questioned by police on Friday following talks with his lawyers.
According to reports, officers are investigating claims against the 58-year-old talent show judge over the alleged incident in a nightclub in Dublin.
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Hide AdWalsh said in a statement yesterday: "It didn't happen so therefore there is no case to answer and I am extremely angry that someone is trying to tarnish my name and reputation.
"My phone has not stopped ringing with messages of support from around the world, which means so much to me. I am hoping that this matter will be resolved as quickly as possible."
Walsh's spokeswoman added: "Louis would like to thank everyone for the overwhelming number of messages of support from around the world that he has received over the last 48 hours.
"He is back home in Ireland and has been co-operating fully with the Garda investigating the allegation." The Irish star, an X Factor judge since 2004, has managed a number of groups and performers, including boy bands Boyzone and Westlife.