The House of Lords Standards Commissioner launched a formal investigation into Cabinet minister Baroness Warsi's expenses claims on Wednesday.
Former police chief Paul Kernaghan decided to investigate after being asked to look into the claims by Lady Warsi.
She is facing allegations that she claimed for accommodation expenses while staying at a friend's house rent-free.
Scotland Yard said it had decided not to investigate Lady Warsi's expenses and had passed the matter back to the House of Lords.
Labour had called for a criminal inquiry into the Tory peer's expenses.
Lady Warsi, the Conservative Party co-chairman, has denied any wrongdoing, insisting that she had acted within the rules at all times.
A spokesman for the Lords Standards Commissioner said today he was holding a formal investigation after an initial assessment.
Scotland Yard said it had "determined that this is not a matter for the police".
"As such the matter has been referred back to the House of Lords Commissioner for Standards," a spokesman said.
"The matter was considered in accordance with previously adopted procedures."
Lady Warsi says she made an "appropriate payment" to her friend - Tory official Naweed Khan, who is now one of her aides - for the nights she stayed at a property in Acton, west London.
But the property's owner, GP and former Conservative donor Wafik Moustafa, denies receiving any income from either Lady Warsi or Mr Khan during the time of her stay in 2008.
At the time, she was claiming Lords subsistence of £165.50 a night.
Baroness Warsi also faces a separate investigation ordered by David Cameron to establish whether she broke the ministerial code.
The prime minister has faced sharp criticism for his decision to refer Baroness Warsi to Sir Alex, the independent adviser on ministerial interests, but not culture secretary Jeremy Hunt.
The Labour Party has said Hunt should be investigated by Sir Alex to see whether he broke guidelines in his handling of News Corporation's bid to take over the satellite broadcaster BSkyB.
Justice secretary Ken Clarke has criticised the media for acting like a "lynch mob" in its pursuit of the allegations against Baroness Warsi and Hunt.
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