Depends on how you interpret being held responsible, not to mention what the challenge is.

Taking the case of brain damage: if a man suffers damage to the part of his brain that manages empathy and social connections and his adrenaline glands pump more adrenaline and testosterone into his body, making him more aggressive. He's naturally going to go on a killing spree, but he can't help it. He's not responsible for his actions, but that doesn't mean we can let him free. He has to be detained, not just for his own protection, but to guarantee the safety of his neighbors.

Law enforcement is built (ideally) to protect society; to protect you from your neighbor regardless of whether or not it's a product of his free will.

Also, while I haven't gotten around to reading the arguments yet, I saw a paper titled that most intellectual scientists and philosophers don't think free will exists, but they don't communicate it to the public. They don't like being told that kind of thing.

Also, most psychopaths actually do suffer from abnormal neurochemistry that impairs social function and empathy. So it's safe to say that they're mentally challenged people who can't help their actions.

The bottom line is, even if they can't be held responsible, they should be detained in one way or another in order to protect the other members of society and guarantee the safety of their persons and their possessions as well.