If an active skill is not affected by cooldown reduction, the hero's info screen will display cooldown reduction as 0%.
This means that even if the hero is equipped with equipment that provide cooldown reduction, the cooldown of the active skill will not be reduced (the hero won't use skills faster).
However, if the hero’s passive skill is affected by cooldown reduction, the cooldown reduction stats from equipment will apply.
Example: If the hero 'Haru' wears an equipment with "20% Cooldown Reduction", the active skill’s cooldown will not reduced, and it will display as 0% on the hero's info screen.
However, the "20% Cooldown Reduction" will increase the number of attack hits.