Criminal Law Questions? Ask a Criminal Lawyer.
It's harrassment, blackmail amongst the other reasons. What state are you in?
It is the burden of proof that the District Attorney in that jurisdiction must decide to indict you or the person who is being accused.
Either way, you will need to establish paternity if you haven't already done so. Since there are no child custody documents, whomever is the primary guardian of the child, you will have to establish the visitation arrangements amongst yourselves, with an attorney or through the Court system.
I don't believe the mother is "actually holding the charges" because the criminal courts either charge you or dismiss you. I think she is not telling the truth. If that you don't know, call the county that she supposedly filed the criminal charge, and ask that County Clerk if there is such a pending criminal charge.
I hope that helps you! Thank you and have a great day!