In the U.S. there is no law that requires you to ever say a word to a law enforcement officer, and lawyers generally encourage you to minimize what you communicate to them anyway.
I can't think of any situation where a request for information could not be demanded in writing. As a practical matter, in some situations you will probably be subject to some extra scrutiny and inconvenience: E.g., in a stop-and-identify situation, you could hand the officer a note saying, "Please make any requests for information from me in writing." The officer may infer that you have some disability, but if he does not (or discovers you don't) he may get irritated enough to subject you to harassment for "contempt of cop".
Of course, if you can understand him, you are still required to obey an officer's lawful orders no matter how they are communicated. But "speak" is not a lawful order.