we "have" crows here......been about 5 years. I love them, i have not lost a chicken to a hawk (not even seen one!) in that time. I have heard they will take eggs, kill chickens but I have not seen it myself. A friend has lost some birst to Ravens, they look like a crow but much biggeer.
I do feed the crows bread 1st thing in the morning, they are out thee waiting for me when I go to do chores. they will call to me in a rattling voice, until I throw the bread down then they will wait till I go in the barn to feed before they come get it. they are pretty neat, and I love the fact they keep the crows away!
*edited to add, I do raise several types of bantams. Some I keep some in the barn caged, but I have a flock of about 30 that are retired show birds or PQ that just free range. Dutch, OEGB and cochins (oh, and a few silkies). I was worried about the smaller birds, but so far so good. every once i a while, there is a momma hen out with her chicks, and so far the water troughs are the only thing that gets one or 2 every now and then.