A 53-year-old man arrested in Hampshire in January, as part of Operation Yewtree - the police investigation prompted by the Jimmy Savile abuse scandal - has been told no further action will be taken against him.
Referring to both the 53-year-old and Jim Davidson, the CPS said there was "insufficient evidence for a realistic prospect of conviction".
The Crown Prosecution Service has explained why it decided not to charge Jim Davidson over alleged historical sexual offences:
We have determined that there is insufficient evidence for a realistic prospect of conviction in relation to all complaints and have advised the Metropolitan Police Service that no further action should be taken.
Jim Davidson is "pleased" to have been told he will face no further action after he was arrested on suspicion of historical sexual offences, his solicitor has said.
The 59-year-old comedian was initially held in January by detectives from Operation Yewtree, the national investigation sparked by the Jimmy Savile abuse scandal, before being re-arrested in March after further allegations emerged.
His solicitor, Henri Brandman, said: "My client Jim Davidson was, of course, arrested a number of months ago in respect of allegations of a historical sexual nature.
"He is pleased to have received news today that there will be no further action relating to the allegations."
Comedian Jim Davidson will face no further action over alleged sexual offences after he was arrested as part of the investigation sparked by the Jimmy Savile abuse scandal, his solicitor said today.
Prosecutors have received full files of evidence in relation to DJ Dave Lee Travis, Jim Davidson and a 53-year-old man who was arrested on 2nd January.
They have also given early investigative advice to police in relation to Rolf Harris, Freddie Starr and Gary Glitter.
The Falkland Islands Government have been made aware of allegations made against Jim Davidson.
We have asked the Metropolitan Police to make enquiries relating to these allegations.
We await the outcome of the investigation.
Jim Davidson's lawyer said the entertainer had not been interviewed over an alleged historic sexual offence carried out in the Falkland Islands.
It was reported today that Scotland Yard detectives were carrying out an investigation on behalf of the Royal Falklands Island Police into an accusation that the comic indecently assaulted a woman while he was on tour and entertaining British troops.
Davidson's solicitor Henri Brandman said: "Jim continues to vigorously deny the allegations that have been put to him and is helping the police as fully as possible in their inquiries.
"Jim has not been interviewed in respect of any alleged incident with a woman suggested to have taken place in the Falkland Islands about 30 years ago.
Davidson, who was yesterday rebailed by detectives from Operation Yewtree, was originally arrested in January over allegations of historic sexual offences against women in the UK.
The 59-year-old has not been charged and has been bailed to July.
Jim Davidson "continues to vigorously deny" allegations of sex offences, his lawyer said after the comedian was rebailed.
Jim continues to vigorously deny the allegations and is helping the police as fully as possible in their inquiries. He has not, of course, been charged with any offence.
Jim Davidson's solicitor, Henri Brandman, declined to comment after his client was rebailed over alleged sex offences.
Davidson, 59, was rebailed to an unspecified date in July.
Comedian Jim Davidson has been rebailed until July over allegations of sexual offences.