The bosses of the BBC and South Yorkshire Police have been summoned before MPs in connection with a recent raid on Sir Cliff Richard's home.
Home affairs select committee chairman Keith Vaz has asked them to explain how the BBC knew of the search in advance.
The BBC says its journalists "acted appropriately" in its coverage but police have accused it of a "cover-up" afterwards over what it had known.
The search related to an alleged sex offence, which Sir Cliff denies.
He has said the allegation of an assault at a religious event in Sheffield in 1985 is "completely false".
BBC cameras and a reporter were outside the gates to Sir Cliff's property in Sunningdale, Berkshire, when eight police officers arrived on 14 August.
The BBC has received hundreds of complaints related to its reporting.
Mr Vaz later wrote to the BBC and South Yorkshire Police asking them to explain what agreement was struck between their organisations.
'Misleading and inaccurate'
In his reply, Chief Constable David Crompton said the force had been approached before the raid by a BBC journalist, who had detailed information about the investigation into Sir Cliff.
He said the force had "reluctantly agreed" to give the reporter prior notice of the raid "in order to dissuade the corporation from publishing details of the investigation".
"It was not done in order to maximise publicity, contrary to some press reports," Mr Crompton said.
He said an article appeared on the BBC News website later on the day of the raid that suggested there had been a "deliberate attempt by police to ensure maximum coverage".
This was "misleading and was known by the BBC to be inaccurate", Mr Crompton said.
He said the force had contacted the BBC, which had refused to withdraw or change the article.
"This appeared to be an attempt by the BBC to distance itself from what had taken place and cover up the fact that it had initiated contact with the force about the story."
In his letter to Mr Vaz on Thursday, BBC director general Tony Hall said "the media has a right to report on matters of public interest".
"The disclosure of a sex abuse allegation against Sir Cliff Richard and the police search of his property was clearly a significant story and the BBC was not alone in providing extensive coverage."
He said the BBC would not provide details about its source or "elaborate on detail of our editorial processes".
And responding to the allegation of a cover-up on Friday, a BBC spokesman added: "The police complained specifically about an analysis piece on the BBC website and subsequently, and highly unusually, we confirmed that South Yorkshire Police was not the source of our story."
After receiving the letters, Mr Vaz said: "These are serious matters which deal with the sensitive issue of how the police conduct their investigations.
"The balance between mass and individual public interest must be struck appropriately and the relationships between the police and the media must always be ethical."
Mr Vaz said the information provided to him in the letters "raises even more questions".
"In his letter the chief constable accuses the BBC of a 'cover-up' which is a matter of deep concern," Mr Vaz said.
He said Lord Hall and Mr Crompton had been asked to appear before his committee on 2 September.
"I have also written to the Metropolitan Police Commissioner to ask him what investigation he is proposing to initiate about how this information was leaked prior to the investigation arriving in South Yorkshire," Mr Vaz said.