She has been accused of breaking electoral law by giving false information about her main residence.
Ms Rayner denies this and Labour leader Sir Keir Starmer said he was "fully confident" she complied with the rules.
The police investigation has been prompted by a complaint from Tory deputy chairman James Daly.
A police spokesperson said: "We're investigating whether any offences have been committed. This follows a reassessment of the information provided to us by Mr Daly."Mr Daly, the MP for Bury North, 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.
'Cooperate with police'
Police initially said there would be no investigation but Mr Daly complained that officers did not appear to have looked at the electoral roll and other documents.
Sir Keir said Ms Rayner has "already given no end of answers in relation to this matter", and that she will "cooperate with the police".
He added: "We welcome this investigation because it will allow a line to be drawn in relation to this matter.
"I am fully confident that Angela Rayner has not broken the rules.
"She will cooperate with the investigation, as you would expect, and it's really a matter for the police."
Asked if we can still expect to see her campaigning over the coming weeks, he said "yes" and added: "We need to let the police get on with their job."
Ms Rayner, nee Bowen, bought the semi-detached home in 2007, getting a 25% discount under the Right to Buy scheme introduced by former Conservative Prime Minister Margaret Thatcher.
The former carer is said to have made a £48,500 profit when selling the house eight years later.
Tax questions
Tax experts have estimated that, while Ms Rayner may not have owed anything in Capital Gains Tax following the sale depending on her residency situation, there are circumstances in which she could have owed as much as £3,500 to HM Revenue and Customs.It is alleged that it would not be allowed for Ms Rayner and her then husband to have both avoided Capital Gains Tax when they sold these properties after they married.
Ms Rayner says she has taken expert tax advice, which she believes confirms her position that no Capital Gains Tax was payable, although she has resisted calls to publish the advice.
Asked earlier this week if he had seen Ms Rayner's tax advice, Sir Keir said: "I don't need to see the legal advice. My team has seen it."
Conservative defence minister Grant Shapps said he welcomed the police looking into the issue again.
He said: "The double standards have been extraordinary, Angela Rayner herself has spent her political career calling people out for exactly the thing that she seems to be doing now.
"It's not acceptable to ignore it and it's not acceptable for Keir Starmer to say he won't even read reports into it.
"This is something which is a serious matter, it's important it's looked into properly. And I welcome the idea that the police are doing that."