Hi,
The tests to be included for Potable Water are covered in American Public Health Association (APHA) in the book called "Standard Test Methods" and includes physical, chemical and microbiological tests.
Btw, for information of everyone, water is generally categorised in many categories; first is Potable (which in layman terms is safe for drinking), while the others are Purified Water, Water for Irrigation, Sterile Water for Injection etc. For these detailed categories and their description, refer to the latest United States Pharmacopoaeia.