It depends on the term "serious crime". For instance, if this term means aggravated assault against a former significant other, then yeah I think it'd be best to come clean and probably pretty soon. If it's a violent crime against someone weaker than you it's not likely going to be well received, but that doesn't mean it'll be an automatic deal breaker. Someone that's voluntarily upfront, open, and honest deserves the benefit of the doubt imo. I don't think you really have an obligation to share the gory details of your past immediately with anyone, but if what you're keeping from her could make her feel in some way unsafe around you, then you're far better off if she hears it from you.
Pain is what the world does to you, suffering is what you do to yourself. Pain is inevitable, suffering is optional.