Technically speaking, you are supposed to turn off the water supply while changing the filter. Practically speaking, however, it isn't usually necessary, as the water is not a continual flow and shouldn't flow in the brief amount of time it takes to replace the filter. The exception would be if the ice maker is currently on. Water will flow when it's time to refill the ice forms and you may have hit the change at that exact moment. I always turn the ice maker off when I am about the change the filter since a very unfortunate incident where I didn't seat the filter properly and left my apartment, causing a flood in my kitchen and my neighbors below me.
