The short answer is yes, you can use your tap water. But before you do, take a piece of your starter and put it in another jar and feed it unbleached flour and use your tap water. If it doubles, continue to do this for at least a week. If it still continues to be active and shows no signs of weakening, your tap water should be safe, but always keep an eye on it. If your tap water is treated with chlorine, you can fill jugs and let the water sit. The chlorine will evaporate from the water after 24 hrs.
Sometimes tap water is treated with a lot of chlorine. If this is the case, it is possible that it will kill the wild yeast in your starter. Some people like to use natural spring water or reverse osmosis processed water.
