Ms Downer, the Liberal party's candidate for the South Australian seat of Mayo, was pictured on social media handing out the prop cheque emblazoned with her image and name for more than $125,000 at a bowling club.

Shadow attorney-general Mark Dreyfus wrote to the Auditor-General, Grant Hehir, on Sunday asking for the matter to be investigated.

"It is completely inappropriate and unacceptable for Ms Downer and the Liberal Party to treat taxpayers' money as if it were their own, and to deceive Australians about the true source of this taxpayer-funded grant," Mr Dreyfus wrote.

He's asked Mr Hehir to investigate the conduct of the Liberal party, Ms Downer and Sport Minister Bridget McKenzie.

Mr Dreyfus said he understood Ms Downer made the announcement to the Yankalilla Bowling Club before local MP Rebekha Sharkie was made aware the funding had been granted.

Ms Sharkie said she had helped the bowling club with getting the grant.

"In more than a decade of politics I've never seen a taxpayer-funded grant delivered by cheque with a candidate's face and name on it. Rather desperate and misleading," the crossbench MP tweeted.

Ms Downer, the daughter of former foreign minister Alexander Downer, was comprehensively beaten by Ms Sharkie at last July's by-election but will try again at the upcoming general election.

Trade Minister Simon Birmingham defended Ms Downer's actions.

"That type of self-promotional act is what members and candidates do right across the country all the time to help raise the awareness of the fact that they're working and fighting for their local community," Senator Birmingham told Sky News on Sunday.

Australian Associated Press