North Yorkshire Police said it began an inquiry into the Jack Raine Community Foundation, in York, in 2016.
The Charity Commission said it was also investigating the charity, which helps vulnerable children and young people.
North Yorkshire Police said a 55-year-old man and a woman, 59, had been arrested and bailed pending further inquiries.
The charity has yet to respond to a request from the BBC for a comment.
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The Charity Commission said after being alerted by the police it had undertaken an unannounced inspection in November 2016.
It found "insufficient financial records and no evidence of trustee meeting minutes to reflect any decisions taken by the trustee board".
It then decided to launch a full statutory inquiry into the organisation.
It will focus on financial management, general administration and whether trustees complied with their legal duties and responsibilities.
The charity's bank accounts have also been frozen in order to protect its assets, the commission added.
Two people have been arrested in connection with a financial investigation into a charity.