I have had friends commit crimes and when they went to a lawyer (who I also am friends with), they were turned away because they did not want to touch the case. The lawyer told me in no way is he going to take a case like that where he knows the potential client to be guilty. Not worth his reputation or time.
She was a court appointed attorney. A public defender. When appointed by a judge, you don't get to turn it down.
From Miranda: "If you cannot afford an attorney, one will be appointed for you"
and
CNN, June 25, 2014: Gibson said Clinton called him shortly after the judge assigned her to the case and said, “I don’t want to represent this guy. I just can’t stand this. I don’t want to get involved. Can you get me off?”
“I told her, ‘Well contact the judge and see what he says about it,’ but I also said don’t jump on him and make him mad,” Gibson said. “She contacted the judge and the judge didn’t remove her and she stayed on the case.”