Police images show the Algarve room after Madeleine disappeared
The parents of Madeleine McCann have accused police in Portugal of exaggerating DNA evidence before naming them suspects in her disappearance.
A UK forensic scientist had already warned DNA in their hire car was "inconclusive", it has been revealed.
His e-mail was in thousands of pages of evidence now been made public.
Madeleine vanished, aged three, on a holiday in the Algarve on 3 May 2007. Kate and Gerry McCann are no longer suspects in the case.
Lack of evidence
The papers, which also include photographs of the family's deserted apartment, make clear that the McCanns came under suspicion following a visit to Portugal by UK detectives last August.
Portuguese police cited DNA evidence as grounds for their suspicions.
Kate and Gerry McCann's spokesman, Clarence Mitchell, said police had told Mr McCann during interrogation that his missing daughter's DNA had been found in the boot of the car - hired 24 days after her disappearance.
The McCann's spokesman Clarence Mitchell says that the files will be investigated privately
The investigation papers show a sniffer dog detected the apparent odour of a body in their hire car and apartment, but tests on a sample from the car were inconclusive.
British forensic scientist John Lowe said the sample contained 15 out of 19 components of Madeleine's DNA which were not "unique to her".
Mr Mitchell told the BBC: "I can confirm in his interview the police put to Gerry as a matter of fact that DNA - Madeleine's DNA - had been found in the vehicle.
"You can see from the official report that wasn't the case. It was inconclusive at best.
"You have to ask yourself what the police were trying to achieve by overstating evidence they simply didn't have in that way to Gerry."
The police inquiry into her disappearance was wound up last month due to a lack of evidence.
The McCanns and a third British national, Robert Murat, were declared to be no longer formal suspects when the police closed the case. The McCanns and Mr Murat, 34, always strongly denied having had any involvement in what happened to Madeleine.
Madeleine went missing in May 2007 days before her fourth birthday
Lawyers for the McCanns, both 40, from Rothley, Leicestershire, were given access to the documents last week.
They are studying the papers for fresh leads that the couple's private detectives could follow up.
Mr Mitchell said: "One of the great frustrations for Kate and Gerry, through all this, was that they just didn't get any information from the Portuguese of any real note at all.
"Now there is a chance to analyse this, and if there's anything that needs priority action in terms of finding Madeleine.
"Such as was this area searched or not? Was there another sighting in a certain place, or not?
"All of that will be moved on quickly. But Kate and Gerry themselves are not fully aware of the mass of detail yet, they're waiting for the lawyers to tell them in due course."
Some 20,000 pages of evidence were released on Monday to journalists who had made a formal request to prosecutors, including the BBC.
The sniffer dog's apparent detection of the odour of a body was followed by a second dog detecting what was thought to be blood in the same locations.
The BBC's Steve Kingstone said the documents showed an initial report from Britain's forensic science service saying the samples indicated some compatibility with the components of Madeleine's DNA.
However the laboratory did not draw firm conclusions and stressed that the samples contained the DNA of more than one person.
In an e-mail dated 3 September 2007, John Lowe of the major incidents team of the Forensic Science Service (FSS) said it was impossible to conclude whether the material taken from the car came from Madeleine.
The McCanns want to follow any leads that come from the police documents
The e-mail was translated into Portuguese the following day and four days later Portuguese detectives named the McCanns arguidos - formal suspects - citing DNA evidence as grounds for their suspicions.
In his message to Det Supt Stuart Prior, head of the British side of the inquiry, Mr Lowe said a sample from the boot of the McCanns' hire car, which they rented 24 days after Madeleine went missing, contained 15 out of 19 of her DNA components.
But he cautioned that this result - based on the controversial "low copy number" DNA analysis technique which uses very small samples - was "too complex for meaningful interpretation or inclusion".
The expert said the components of the missing girl's DNA profile were not unique to her - in fact some were present among FSS scientists, including himself.
"We cannot answer the question: is the match genuine, or is it a chance match," he wrote.
Subsequent interview transcripts reveal that Kate McCann was asked directly: "Did you have anything to do with the disappearance of your daughter?"
She refused to answer this and dozens of other questions, as was her legal right.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.