Should I rinse chicken livers before cooking them? I bought some fresh packed chicken livers from the supermarket (refrigerated). At home I froze them. Today I've thawed them and they were bloody. I've put them into a bowl with cold water, then drained them. The water was reddish and small pieces of tisue were floating.

Was my approach ok/safe? How is it done in restaurant kitchens?
Should I just drain the blood and water after thawing or wash them with cold water?
You should prepare the chicken livers by trimming away any fat, sinew, etc. You shouldn't need to rinse them, but it's OK to do so. Just be aware any time you are washing chicken or chicken parts that the bacteria can get all over your sink and kitchen, so I generally just confine to the cutting board and then wash it with warm, soapy water or put into dishwasher.