You can overdose but you have to add a lot more than the recommended amount (10 times the amount).
This happens a lot when water companies do work on the pipes. They increase the chlorine/ chloramine level after the work is done to make sure nothing is alive in the water. Then people do a water change on their fish tank (within 24-48 hours of the work being done) and the fish either die or get black marks. The black marks usually clear up within a month.
The water company does not have to tell you they are working on the pipes and some companies regularly increase chlorine/ chloramine levels when the weather is extremely hot, or if they have dam water and it rained really heavily.