Safe level of chlorine in water
Chlorine is a reactive substance and an oxidizing agent. It can cause damage to surfaces exposed to it such as eyes, skin etc but it cannot penetrate deeper. Chlorine can damage your hair by oxidation — hair becomes rough and brittle. This is not same as hair loss — chlorine doesn't cause hair to fall out because it cannot penetrate to the follicles. See here

EPA has set maximum residual disinfectant level for chlorine (as Cl2 and other chlorinating agents such as chloramine [NH2Cl] and chlorine dioxide [Cl2O]) beyond which it is considered unsafe.

Chloramine       :  4.0 mg/L or 4 ppm
Chlorine         :  4.0 mg/L or 4 ppm
Chlorine Dioxide :  0.8 mg/L or 800 ppb