The sex offence allegation against singer Sir Cliff Richard is reported to have taken place at a rally for a US evangelical Christian preacher in 1985.
The Berkshire home of Richard was searched by police over allegations a boy under the age of 16 was abused at an event held by Pastor Billy Graham.
The event took place at Bramall Lane, the home of football club Sheffield United. No one was arrested as part of the search and Richard was not present at the time.
It is not known if Richard, a devout Christian, attended the rally by Graham, who is known to be friends with former US president George W Bush, as well as counselling other US presidents.
A statement on Graham's website said Bush told him on his birthday in 2008: "Some years ago, God used you to change my life."
Richard and Graham are known to have been friends for many years. It was at a Graham campaign meeting in 1966 that Richard first announced he was a Christian.
The 73-year-old denies the "completely false" allegations and criticised South Yorkshire Police for going to his home in Sunningdale without any notice.
Richard, who is currently in Portugal, said: "For many months I have been aware of allegations against me of historic impropriety which have been circulating online.
"The allegations are completely false. Up until now I have chosen not to dignify the false allegations with a response, as it would just give them more oxygen.
"However, the police attended my apartment in Berkshire today without notice, except it would appear to the press.
"I am not presently in the UK but it goes without saying that I will cooperate fully should the police wish to speak to me.
"Beyond stating that today's allegation is completely false it would not be appropriate to say anything further until the police investigation has concluded."
The search was conducted by South Yorkshire Police officers with the help of Thames Valley police.
The investigation is not part of Operation Yewtree, the Metropolitan Police inquiry looking into sex offence allegations in the wake of the Jimmy Savile scandal.
A South Yorkshire Police spokesperson said: "South Yorkshire Police has gained entry to a property in the Sunningdale area of Berkshire.
"Officers are currently searching the property.
"A search warrant was granted after police received an allegation of a sexual nature dating back to the 1980s involving a boy who was under the age of 16 at the time.
"No one has been arrested and the owner of the property was not present."