Generally, a LEO is free to approach you and ask questions for any reason whatsoever, or no reason at all. And generally, you have the right to refuse to answer.

However... if the LEO questioning is part of airport security, I suppose the consequence of remaining silent could be that you don't fly. Whether that will be case, and whether such a penalty would "fly" (heh-heh) with the courts, I don't know. I'm inclined to think that if the questioning is restricted to situations where the LEO has at least "reasonable suspicion" that you're up to no good, then the courts would be more likely to allow a no-fly punishment for pax who won't chat with Officer Friendly.