Tap water frequently has elements, such as chlorine, in concentrations that can be damaging to plants. The same applies for well water. However, this is not always the case. Water quality varies from area to area. Also, plants have varying levels of tolerance for certain minerals.
Many gardeners never have any problems using tap water.
The only way to be sure would be to have a water quality analysis made. However, these are expensive and unrealistic for most gardeners. You could just try using your water source as a test to see how it effects the plants. One good experiment would be to grow two plants and use your tap water for one plant and feed the other plant with distilled water. Then document the results.