Yes they do. In fact you can buy a water conditioner made just for reptiles & amphbians, but it's the same stuff that is used for fish.
You know how chlorine in a swimming pool iritates your eyes? now imagine your eyes being 100 times more sensitive to chlorine and you'll understand why turtles need it to be removed.
Interesting fact: some turtle species can draw water in through the anus and extract oxygen from the water into blood capillaries in the walls of the rectum, effectively breathing through their arsehole. That's another area that would be VERY prone to irritation from chlorine (and ammonia in fouled water).