Pure water as it does not has ions it wont conduct current. So electrolysis of distilled water is not possible. By adding impurities in the form of salt we can do the electrolysis. Because salt when added to water exist as ions.
For ex
NaCl + H2O -----> Na+OH- + H+Cl-
So the electrolysis of water can be carried out
2 NaCl + 2H2O ------> 2 Na+ + 2 OH- + Cl2 + H2
So
If distilled water is used as an electrolyte there will be no evolution of hydrogen gas and dissociation of sodium and chlorine ions.