The veteran pop star voluntarily met members of South Yorkshire Police over the weekend, and was not arrested or charged.
South Yorkshire police said they had spoken to a 73-year-old singer.
His Berkshire apartment was searched by police as part of the investigation into an alleged sexual assault at a religious event in 1985.
A spokesman for Mr Richard yesterday said: “Today, Sir Cliff Richard voluntarily met with and was interviewed by members of South Yorkshire Police. He was not arrested or charged.
“Other than restating that this allegation is completely false and that he will continue to co-operate fully with the police, it would not be appropriate for Sir Cliff to say anything further at this time.”
Mr Richard was in Portugal when the search took place on August 14. His fans have rallied round the veteran star and are showing their support by buying copies of his 1992 top 10 hit ‘I Still Believe In You’ with the song headed for this weekend’s Top 40.
It emerged earlier this week that he has pulled out of a visit to the US Open tennis championships and turned down the freedom of his adopted Portuguese home city of Albufeira.
Mr Richard also cancelled an appearance at a charity fundraising event at Canterbury Cathedral next month because he did not want the event to be “overshadowed by the false allegation”.
Meanwhile the BBC has been accused of a “cover-up” over its role in the raid by officers from South Yorkshire and Thames Valley police.
South Yorkshire police chief constable David Crompton claimed that the broadcaster appeared to “distance itself from what had happened” after it broadcast the raid on the pop star’s penthouse.
The BBC, which had a film crew on the scene, broke the news of the search but has been heavily criticised for its handling of the story.
Mr Crompton said that the BBC’s misleading and inaccurate portrayal of its involvement in what happened led to the force making a formal complaint.
Mr Crompton said that an article appeared on the BBC website on the afternoon of the raid that suggested there had been a deliberate attempt to “ensure maximum coverage” by the force.
Keith Vaz, British home affairs committee chairman, said the claims were a “matter of deep concern”.
He has summoned the chief constable and BBC director general Tony Hall to appear before the committee on September 2.
Mr Hall has insisted that BBC journalists “acted appropriately” in its coverage of the story.
A BBC spokesman said: ”We have set out our position. The story was clearly in the public interest. The police complained specifically about an analysis piece on the BBC website and subsequently, and highly unusually, we confirmed that South Yorkshire Police was not the source of our story.”