One thing I will suggest. Get a cheap OTO test kit (chlorine comparator is shades of yellow) and test your water. If there is truly no chlorine the test will stay colorless. As states above all other forms of testing (Including FAS-DPD and syringaldazine/vanillin used in the majority of test strips) can and will bleach out at very high chlorine levels leading you to believe that there is no chlorine when there actually is. This is just a backup to make sure that there really is no chlorine in the water. If the test turns yellow, orange,m or brown then there is chlorine.
Other then that follow the excellent advice that Ben gave you.