I think a lot depends on one, the nature of the crime, two, the spiritual deliverance of the person and three the attitude the person presently has toward their crime.
For one some crimes like sexual predator goes deep to the very heart of a person. Sex is at the heart of a person. We all start off with a healthy, innocent and pure notion of sex until someone taints it by these vial acts.
You have to seriously break down some social and personal barriers for a man to molest a child. God can forgive but that goes to point two, the person has to seen the heinous crime for what it really is exceeding wicked. Even then its kinda scary to fully trust them. I have close friend today who's mother married a man that eventually molested her and mother did not take it serious until later.
Then their is three, The attitude or disposition one takes toward an object, subject or matter? Is he still secretly hugging it in his heart such as a porn site? Has he changed his attitude toward it? Does he see the wicked nature of it and how it has all but destroyed his life? Even with all this, you would need to seek God and Godly counsel. Would you want to take on this type of past?