The phrase "a statement alleging that" is correct and usable in written English.
It can be used in legal or formal contexts when referring to claims or accusations made about someone or something.
Example: "The report included a statement alleging that the company had engaged in unethical practices."
Alternatives: "a claim asserting that" or "an accusation stating that".
By way of explanation, the Obama campaign released a statement alleging that "Romney's business strategy wasn't about strengthening companies and creating jobs for long-term economic growth.
On the day that his allegations forced Fifa to investigate their president, Sepp Blatter, for breaches of their ethical code, Mohamed bin Hammam has released a statement alleging that "there is increasing evidence of a conspiracy against his candidacy for the Fifa presidency".
On Wednesday, a second former TERI employee released a statement alleging that Pachauri repeatedly sexually harassed her at TERI from 2003 to 2005.
West Midlands Police have released a statement alleging that they were called to the university because of an assault: "Officers arrived at Senate House at 4.50PM to find a group of around 25 students protesting about fees and a staff member reported that he had been assaulted by one of the group.
Drohobyczer's statement alleged that LaVerne Toney had misappropriated millions of dollars, had been untruthful, had "undue influence" and was unqualified to serve as executor of the estate.
But on Saturday, parties running against Mrs. Johnson Sirleaf issued a statement alleging fraud and saying that "if the process continues we will not accept the results".
However, there are some who read your statement, alleging that you represent the players, as a deliberate and provocative challenge to the integrity and independence of the players and their duly elected representatives".
The Saudi statement alleges that the recent protests were stirred up by an unnamed foreign power, by which it invariably means Iran.
The statement alleged that the commission was being threatened and intimidated by persons "holding different status".
The statement alleges that she was "sexually abused by both players" and "physically assaulted by both".
His statement alleges that he found himself dealing with what he describes as unwanted behaviour by the cardinal after a late-night drinking session.
