Here's the way I understand it ....
Some people claim that the chlorine that is put in to tap water is harmful to your plants. People would let the water sit out in a bucket for 24-48 hrs to allow the chlorine to evaporate out of the water. A lot of cities have switched to using chloramine instead because it does not evaporate like chlorine does, so growers have turned to using RO water now.
The chloramine does not do harm to your plant per se, but there is a theory that it will in fact disrupt (or even kill if high enough ppm) your micro-heard of beneficial bacteria in your soil if you are growing organically.
I have been using tap water for my plants for a long time, and I have seen no adverse effects from it. I do let the water sit out for 24+ hours before using it, but honestly I don't even know if that is necessary. Perhaps the only benefit to that is allowing the water to reach room temp before using it.
If you're growing organically, then you should check with your city to see if they are using chlorine, or chloramine. If they are using chlorine, let your water sit out before using it. If they are using chloramine, you may want to consider a RO unit. If you are not growing organically, then my hunch would be you have nothing to worry about.
I'm trying my hand at organics as we speak. I will let you know if I see any adverse side effects form the water....