Do you need to rinse liver?
I can't speak to health reasons (and we don't answer health related questions on SA) but, as for taste, rinsing chicken livers can be quite important. 

I always rinse and check the chicken livers well to be sure that there are no gallbladders (or pieces) left attached to the liver. The gallbladder contains bile and even a small piece can ruin the taste of the whole pot. Please see  this .