I have had a female ( I think ) Coopers visiting my bird bath for about 3 weeks now., she is there just about every day.
I have had her and a mature male and an immature at one time in the back yard.
I have seen a Coops pick up a squirrel a few times in the past on a neighbor's lawn, but my local squirrels ignore her.
I would think that squirrels would be a prey species for Coops but my tree rats don't give her any respect.