The House of Lords standards commissioner launched a formal investigation on Wednesday into Cabinet Minister Baroness Warsi's expenses claims.
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 Party co-chairwoman's expenses.
Lady Warsi has denied any wrongdoing, insisting that she had acted within the rules at all times.
Prime Minister David Cameron ordered a separate inquiry on Monday into whether she breached the ministerial code when she was accompanied by a business partner on an official visit to Pakistan.
The PM called in his independent adviser on ministerial interests Sir Alex Allan to investigate after she admitted failing to disclose her business relationship with Abid Hussain.
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