Claassen has pleaded not guilty to charges of endangering the welfare of a child, trespassing, and criminal impersonation.
She is set to appear in court again on June 15.
While her Facebook profile claims she has a daughter, police have been unable to verify whether this is true.
According to ABC News, officials from New York City Public Schools have released a statement since the incident, saying, “Enrolment fraud is a serious crime that fundamentally undermines New York City Public School values.
“The NYPD is actively investigating these allegations and will pursue all appropriate legal action against those responsible. We are providing all necessary and suitable support to the school community.”
The student newspaper for the neighbouring Bronx River High School said Westchester Square officials were in the process of reviewing school enrolment procedures.