Christine Lacson Abad, 27, of Cary, North Carolina, was charged with arranging a child sex offence, attempting to groom a 15-year-old in Wrexham and two more sex offences.
But the Crown Prosecution Service said it was no longer pursuing the case.
It said the decision followed further information from North Wales Police.
A spokesman for the CPS added: "Having undertaken this review, it is not now considered that there is a realistic prospect of obtaining a conviction and accordingly, a decision has been made to stop the proceedings."
An American woman accused of travelling thousands of miles to commit a child sex offence in north Wales has been cleared after her case was dropped.