Some people just leave them in a paper bag and store them in a pantry, but ideally they should be kept refrigerated. If possible, take them out of the refrigerator 24 hours before you plan to use them and let them come back to room temperature.
You can certainly keep potatoes in the refrigerator if you choose, but you do not have to unless your house if very hot. Generally, you want to keep potatoes in a relatively cool, dark, dry spot.
Potatoes are not stored in refrigerator.They are stored out in the air. While air touches these they keep fresh.The best way to store potatoes is in the fresh air.