Distilled water is purified water, so both distilled water and other forms of pure water have approximately the same conductivity. The conductivity of distilled water is relatively low, since conductance depends on the amount of dissolved solids in the water, such as salt.
Distilled water is purified through a filtration process that strips it of contaminants and minerals. Pure water does not have any elements besides oxygen and hydrogen. Distilled water may have some more conductivity than other types of pure water if the distillation process has not completely removed the dissolved solids. Tap water and sea water have much better conductivity than distilled water.