Usually, it is not up to the parents. Depending on what you are being charged with, the statute of limitation, usually, can be from one year up to 3 years as a felony. Although, there are other penal codes that have longer statutes. Unfortunately though, you already spoke to the detective and there was no obligation for you to do so.
Your best bet is to figure out how to mitigate your charges and try to get out of this without any jail or possibly prison time. You may have to register as a sex offender, but, this all depends on what you are going to be charged with.
This is a very scary situation to be in.
If you have any questions, please do not hesitate to contact me
You need an attorney ASAP ! Do not speak with anyone other than your attorney . The girls parents cannot drop the charges. This is serious. Call me with any questions.
Get an attorney ASAP. Do not talk about the facts of this case with anyone else. They may not have had enough to convict you before you made those statements to the police. Now your case is much more complicated.