The email was alleged to have disparaged Nick Daubney, Conservative leader of West Norfolk Council.
Mr Murphy was accused of telling council officer Kevin Vaughan to send the email disparaging Mr Daubney.
Mr Murphy said the complaints had come from third parties, and that Mr Daubney had never complained about him directly.
Mr Daubney has called on Mr Murphy to stand down permanently, claiming the email was a "serious attempt to undermine my position".
It referred to Nick Daubney, the Conservative leader of West Norfolk Council.
The standards hearing, held on Friday, was investigating the sending of an email which allegedly disparaged Nick Daubney, the Tory leader of West Norfolk Council.
However, Mr Murphy was cleared of various accusations relating to an email sent to the BBC disparaging Nick Daubney, Conservative leader of West Norfolk Council.
It was sent two days before Mr Daubney was due to appear on the station to discuss a proposed waste incinerator at Saddlebow, King's Lynn.
Mr Murphy was censured for allegedly sending an email which undermined a fellow Tory, the leader of King's Lynn and West Norfolk District Council, Nick Daubney.
The complaints against Mr Murphy relate to an email sent by Kevin Vaughan, a Conservative political assistant at County Hall, regarding West Norfolk Council's Conservative leader, Nick Daubney.
It was sent two days before Mr Daubney, leader of West Norfolk Council, was due to appear on the station to discuss a proposed waste incinerator at Saddlebow, King's Lynn.
The email, released after a Freedom of Information request, said that Mr Daubney was facing "a serious leadership challenge" and that his council had failed to procure alternative technology to the plant.
In the email, released after a Freedom of Information request, Mr Vaughan suggested it might be "pertinent information" for presenter Nick Conrad to know that Mr Daubney was facing "a serious leadership challenge".
The email, released after a Freedom of Information request by Mr Daubney, suggested it might be "pertinent information" for the presenter to know that Mr Daubney was facing "a serious leadership challenge" and that West Norfolk Council had not come up with an alternative to the incinerator.
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