Never use distilled water for any animal. Distillation removes ALL the minerals and electrolytes from the water which is NOT a good thing for drinking water. Its important to note that there is a difference between bottled drinking water and distilled water. Bottled drinking water is filtered. Distillation is a process of evaporating the water into steam and then condensing it back into a liquid. Bottled drinking water is fine if you want or need to use something other than tap water. I've never used anything other than tap water for my animals.
Steve