He sounds like a first-class jerk and if I were you, I would ditch him and find someone that you can trust, someone that won't run from the truth, someone that will communicate with you. You are just setting yourself up for a lot of hurting with this guy.
If he won't talk about it he probably has a guilty conscience. Communication is very important in a relationship. Don't play games. If you can't trust him, just move on. You might want to consider your reasons for your suspicions. If they are valid and he won't talk about it just move on. That is not a basis for a good relationship.