A public water system should follow your state radon program and remove radon according to the standard set out there. You can check your annual water quality report to see how much radon is currently in your water supply.
If you want to learn more, you'll first need to find out whether your provider gets your water from a surface source, such as a lake or a river, or an underground source. There's a higher possibility that your water supply contains radon if it comes from groundwater. In this case, you can contact your water supplier and ask if they test and/or treat the water for radon according to your local radon program.
If your supplier doesn't test for radon, you may want to do so yourself for peace of mind.