Labour’s deputy leader Angela Rayner says she will step down if she is found to have broken the law.
In a statement, she said she was “completely confident I’ve followed the rules at all times”.
She has been accused of giving false information about her main residence in a row about who lived in her former council house.
Greater Manchester Police (GMP) are investigating whether any crimes have been committed.
In a statement released by the Labour Party, 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 MP, who is also Labour’s shadow housing secretary, said she looked forward to setting out the facts with the relevant authorities as soon as possible.
She added: “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.”
The police investigation has been prompted by a complaint from Tory deputy chairman James Daly, who is understood to have made police aware of neighbours contradicting Ms Rayner’s statement that a property, separate from her husband’s, was her main residency.
Police initially said there would be no investigation but Mr Daly, the MP for Bury North, complained that officers did not appear to have looked at the electoral roll and other documents, nor spoken to neighbours.
A spokesperson for Greater Manchester Police said: “We’re investigating whether any offences have been committed. This follows a reassessment of the information provided to us by Mr Daly.”
The force did not provide further details of its investigation.
Ms Rayner, nee Bowen, bought a semi-detached council home in 2007, getting a 25% discount under the Right to Buy scheme introduced by former Conservative Prime Minister Margaret Thatcher. She is said to have made a £48,500 profit when selling the house eight years later.
The former carer was registered as living at that house, on Vicarage Road, Stockport, in Greater Manchester, on the electoral roll until she sold the property in 2015.
But she appears to have given two different addresses when she re-registered the births of two of her children in 2010 following her marriage to Mark Rayner, listing her then-husband’s home on Lowndes Lane.
Which home was her main residence is at the heart of the row, with tax experts estimating she may owe up to about £3,500 in Capital Gains Tax in the worst case scenario – although she may owe nothing at all.
Ms Rayner said she would “make no apologies for having held Conservative ministers to account in the past” and added “we have seen the Tory Party use this playbook before – reporting political opponents to the police during election campaigns to distract from their record”.
In 2022, her party leader Sir Keir Starmer, was reported to the police by the Conservatives over allegations he had breached lockdown rules in the so-called “Beergate”. He was later cleared.
Earlier, Sir Keir said he was “fully confident that Angela Rayner has not broken the rules”.