The phrase "a statement to the effect" is correct and usable in written English.
It can be used when referring to a statement that conveys a particular meaning or implication without quoting it directly.
Example: "The witness provided a statement to the effect that he saw the defendant at the scene of the crime."
Alternatives: "a statement indicating" or "a statement suggesting".
Will James issue a statement to the effect that she was misunderstood and loves the younger singer?
This is not something you can be in much doubt about: he has a statement to the effect tattooed on his neck.
He said that Mr. Golden's grandmother, Juanita Lumpkin, had "made a statement to the effect of nobody loved him and he was going to kill himself".
Acknowledgments typically open with a statement to the effect that, although writing is lonely work, the author could never have completed his book without help and support.
"Police Scotland has today, however, put out a statement to the effect that I 'will appear in court at a later date'.
I am a rational man and I just made a statement to the effect that Osama bin Laden and his group are soon to die because of their own actions.
McCabe called the Russia investigation "highly significant," while White House spokesperson Sarah Huckabee Sanders issued a statement to the opposite effect Wednesday.
Minority Leader Mitch McConnell (R-KY) issued a statement to the same effect, griping that "the majority somehow convinced the parliamentarian to break with the long standing precedent" of the chamber.
Hours later, the Sanders campaign released a statement to the same effect, but also called for the government to declassify a not-yet-released section of a report produced by a Senate inquiry into events leading up to and immediately following the attacks.
European donors have consistently monitored our textbooks to ensure that they are satisfied; in a statement to that effect, the EU states that the "new textbooks, though not perfect, are free of inciteful content and improve the previous textbooks, constituting a valuable contribution to the education of young Palestinians".
Lenin's niece, Olga Ulyanova, even made a public statement to the effect that it was a bare-faced lie that her uncle had wanted to be interred with his mother.
