The rain probably will dilute your chlorine, albeit only a little--unless it's a storm with lots of wind that would blow debris into your pool. It shouldn't affect any of the other readings. So whether to cover it or not is up to you--do you need the water replenishment, or do you need to keep debris from blowing into the pool? If it's just passing rain showers, I'd leave it uncovered, but that's just my opinion.

Janet