It depends on whether she is mentally competent or not; people can have certain mental disorders while still being competent.Assuming the girlfriend is old enough (of legal age to consent to sex and  marriage) and had *not* been legally determined to be mentally incompetent (e.g. has not had a legal guardian or conservator appointed for her by the courts), then she can make her own decision who to marry, and if she wants to marry you, the two of you can marry. However, if she is underage she cannot legally consent to marriage; or if she of age, but has been determined to be mentally incomptent (has a guardian, etc.), then she cannot marry you, because mentally incompetent people cannot enter into legally valid marriages.