Greater Manchester Police are investigating whether Labour deputy leader Angela Rayner broke electoral law.
Rayner is accused of providing the wrong information about her living arrangements.
The police inquiry was launched following a complaint from deputy Tory chairman James Daly.
A spokesperson for GMP said on Friday: “We’re investigating whether any offences have been committed.
“This follows a reassessment of the information provided to us by Mr Daly.”
In 2010, after she got married, Rayner lived in an ex-council house in Stockport that she had bought in 2007.
According to a biography of Rayner by former Tory chairman Lord Ashcroft, she was registered on the electoral roll as living at the same address until she sold the property in 2015.
However, she is accused of actually living at her husband’s house nearby, leading to claims that the profit she made on her property should have been subject to capital gains tax.
The force had previously said it would not launch an inquiry into the allegations.
Rayner has strongly denied any wrongdoing and Labour said she “welcomes the chance to set out the facts with the police”.
Keir Starmer has accused the Conservatives of trying to “smear” his deputy with the allegations.