In a statement, Brewster School Superintendent Valerie Henning-Piedmonte said the district was notified of the relationship on Thursday and immediately contacted law enforcement, which began an investigation.
"Student safety is of paramount importance and we find these allegations deeply troubling," Henning-Piedmonte said.
During the investigation, Henning-Piedmonte said the staff member involved will not have any contact with students.
The district has arranged for school counselors to be available to support students should the need arise, she added.
In addition, in conjunction with the Sheriff's Office, the district has set-up a 24-hour hotline for anyone who may have information to share about the matter.
The hotline number is 845-808-4377.
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