Which state's law would apply depends on where the sexual activity took place ... if in her state, the age of consent at 16 would apply ... if in your state, the age of consent at 17 would apply.
The threat by her family is in itself quite possibly a criminal
act. New York Penal Code section 135.60 defines criminal coercion as:
Section 135.60 Coercion in the second degree
A person is guilty of coercion in the second degree when he compels or induces a person to engage in conduct which the latter has a legal right to abstain from engaging in, or to abstain from engaging in conduct in which he has a legal right to engage, by means of instilling in him a fear that, if the demand is not complied with, the actor or another will:
4. Accuse some person of a crime or cause criminal charges to be instituted against him;
Coercion in the second degree is a class A misdemeanor.
There is a defense to this crime:
Section 135.75 Coercion; defense
In any prosecution for coercion committed by instilling in the victim a fear that he or another person would be charged with a crime, it is an affirmative defense that the defendant reasonably believed the threatened charge to be true and that his sole purpose was to compel or induce the victim to take reasonable action to make good the wrong which was the subject of such threatened charge.
Under the circumstances, however, it does not appear that this defense would apply.
You should be careful about referring to this court section ... just tell them that you are aware of it and want them to stop threatening you. Do not make any counter threat to file a complaint against them.
If you committed no crime, it doesn't really matter what report they make. Good luck to you in this difficult situation.