Well from my life experiences generally anything with batteries in it, has an ON/OFF switch. Usually the way it works is, when the device is ON, the batteries are being drained. I am sure most mice like that have a power save feature, but I never trust it. To me, it's just common sense, and I'll ask the question: "Do I want to waste my batteries by leaving this on, or do I want to save the batteries and turn it off when I'm not using it?"
So my answer would be to turn it off. Even if it has a power save feature, turn it off, even if it has an ON/OFF switch.