Water out of your faucet is generally very clean, from a bacterial point of view. Unless you know better from experience with your water source, I wouldn't worry about it.
Boiling water also removes a lot oxygen from it (hence why it's better to wash yeast with boiled water....along with the sterilization), which could dampen its ability to 'wake up' when rehydrating (this last point I am way less sure about)
I will add that my apartment I hate my faucet water, and anything that I need to use for brewing after I run out of Meijer Spring Water (only the best!) is after running it through a Brita filter.