Hyejeong Shin, from New Brunswick in the state, has been charged with one count of providing a false government document with the intent to verify one's identity or age, NBC News reports.

Police said she showed a false birth certificate "with the intent to enrol as a juvenile high school student".

"Last week, by filing some false documents, an adult female posing as a student was able to be enrolled in our high school," New Brunswick Public School District Superintendent Aubrey Johnson said at a board of education meeting.

During her days in school, Shin spent a lot of time with guidance counsellors who were trying to find out more information about her, Mr Johnson added.

He said staff members at the school "uncovered this woman's ruse and enabled us to address this situation promptly".

"Once our staff determined it was dealing with fraudulent information, they immediately notified the appropriate authorities. The individual in question has now been charged," Mr Johnson said in a statement on Wednesday.

The school has warned students to refrain from having any further contact with the woman, in person and remotely, he added.

Mr Johnson said the district will take a look at its enrolment process to better identify false documentation.

"This is an unfortunate event. Communication has been provided to the parents of individuals that the young lady may have come into contact with, and communication has been provided to all high school parents today," Mr Johnson said.

Police have said schools are required to "immediately enrol unaccompanied children, even in the absence of records normally required for enrolment".

However, a district can request such documents later to verify a student's age.

The Middlesex County Prosecutor's Office said it is not investigating the incident.

It was not immediately clear whether Shin has a lawyer.