How many videos have we seen where this could come in handy?
My recommendation when beginning to record someone, especially a police officer, is to start with the statement, "I want you to know you are being video and audio recorded." When they tell you to shut it off, ask simply, is it against the law to record you? They may say it is or not, (in NH it is against the law to audio record) and you can choose your fight there, but don't fight them on such a meaningless issue. You are still recording them and you told them so (with your video pen).
Let them think they got you to shut off your camera and cooperate, but ask pointed questions like any good journalist would. Think in advance what questions you would like answered. Think in advance what answers they will give and what your next question will be.