Greater Manchester Police is looking into claims that Labour's deputy leader may have committed an offence by giving false information on where she was living.
It comes after questions over whether she mispaid capital gains tax over the 2015 sale of a property in Stockport.
Ms Rayner said: "If I committed a criminal offence, I would of course do the right thing and step down.
"The British public deserves politicians who know the rules apply to them. The questions raised relate to a time before I was an MP and I have set out my family's circumstances and taken expert tax and legal advice.
"I look forward to setting out the facts with the relevant authorities at the earliest opportunity." It came after Labour leader Sir Keir Starmer was left squirming when he was asked three times if she should resign as his deputy if found to be in the wrong.
In an awkward TV interview Sir Keir insisted Ms Rayner had given answers on the issue, yet he dodged questions about her future.
Labour said it remains completely confident" she has complied with all the rules. Police re-examined a decision not to investigate after a complaint by Tory MP and deputy chairman James Daly.
spokesperson A police said: "We're investigating whether any offences have been committed. This follows a reassessment of the information provided to us by Mr Daly." Speaking to ITV Sir Keir refused to say if Ms Rayner should quit if she is found to have broken the law.
He said: "She's given answers on the issue many, many times over, she's clearly said she'll co-operate with the police.
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