it does bt very very little or acts as bad conductor as compared to sea water or tap water....the reason behind this is the lack of salts or any mineral...we knw that in any liquid electricity is produced when +ve or -ve ions move frm one electrode to another with some charges carried by them....sea water contains salt in it, which readily ionizes to ions of na+ or cl- that flow through water with chareged particles thus conduct electricity... but distilled water is form of water that is boiled to steam and recondensed again to water and its same as pure h2o ....thus it dont show conductivity of electricity..

OK means that it doesn't dissociate ions in fresh water