Do you really need to defend yourself against a minor crime like violating curfew? While you may not think it's that important, breaking curfew can be used against you in court, so it's best to avoid any violation on your record. In a worst-case scenario, you could go to jail for breaking curfew. Generally speaking, curfew violations are handled by the city or county government without such a punishment, but they are enacted to prevent crime and can carry serious penalties.
If you're accused of a sex crime, the last thing you'll want to have describe your innocence or guilt is a psychological test. Tests are not infallible, and they simply can't replace hard evidence of a crime.
Sex offenses take many forms, none of which is particularly good to be charged with. Whether the offense you're accused of is sexual assault or having child pornography, your reputation is at serious risk. It's easy for someone to make an accusation, but the damage it can cause to your reputation if you don't defend yourself is not easy to repair.
Is statutory rape something you can really face charges for? The answer is yes, even if you're close in age to the minor who was allegedly raped. Statutory rape doesn't require force and simply means that one of the people involved in the sexual act was under the age of consent. If the child or minor is coerced or forced to participate in the act, then it's likely you'd be charged for molestation or aggravated rape, not statutory rape.