The singer, 75, said he was left physically and emotionally exhausted by a two-year ordeal that began when South Yorkshire Police raided his home live on BBC television.
Richard told the Daily Mail he is now undergoing medical tests to establish if he has suffered any long-lasting ill effects.
Describing one episode the day after the police search — referred to by him as “the break-in” — the famously keen tennis player told how he was taken ill on the court.
He said: “I went ahead, but I could hardly lift my arm up. I was told: ‘Just take it gently’, but I couldn’t do that either. I couldn’t understand what was happening to me. I thought I was going to die.”
The veteran entertainer was at his farm and vineyard in Portugal in August 2014 when he received a call saying police officers had a warrant to search his Berkshire apartment.
However, he was unaware of what he had been accused of until coverage of the raid appeared on BBC News.
He told the newspaper: “That’s when I discovered what I was supposedly accused of.”
The star described how the following day, with the media outside his home, he collapsed.
“I didn’t know how I could face the future or face my friends or face my family. I was in tears,” he said.
“I was on my knees in tears in the kitchen. Somebody got me to my feet and said: ‘You’ve got to stand up, you are not guilty, hold your head up, you can do it.’”
The case against Richard was dropped earlier this month after a review of the evidence by the Crown Prosecution Service.
South Yorkshire Police have apologised over their handling of the investigation, during which the veteran star said he felt like he was “live bait” for accusers with spurious claims.