A woman in February claimed though the media she had been sexually abused by the 66-year-old as a teenager over a six-month period when she was living with him and his wife over a six-month period 40 years ago.

Mr Hidding strenuously denied the allegations and said it was a malicious attack which was based on a dispute between the woman and his family.

Police in a statement on Monday said no charges would be laid

"Advice was sought from the DPP who reviewed the available evidence and determined that given the constraints posed by the passage of time and the resulting impact on the evidence available, there was no reasonable prospect of conviction," they said.

Mr Hidding said he made a tough decision six months ago to retire from politics after the abuse allegation was published.

"Today, my wife and I are pleased to have been advised that an exhaustive examination by the law and justice authorities in Tasmania has resulted in a decision that no action will be taken in regards to the matter," he said.

"We look forward to the next, more positive, chapter in our lives, wherever life takes us."

Mr Hidding said he was grateful to have received support from across the Tasmanian community and political divides.

He said it was his long-held stance that anyone who had genuine concerns about incidences of sexual abuse to report those matters to the police.

Liberal Party state president Geoff Page said the party welcomed the decision made by Tasmania Police and the finalisation of the matter.

"It is extremely unfortunate that this matter clouded Mr Hidding's retirement from Parliament after a long and stellar parliamentary career," he said.

"No doubt this has been a very difficult time for all involved."