Datoria Dunlap, 17, dropped the note Monday morning in a stairwell of Amityville Memorial High School, where a staff member found it about 8:30 a.m., leading to an evacuation, court documents show.
She was charged with second-degree false report of an incident. Bail was set at $2,500 cash or $5,000 bond.
Video surveillance showed the 11th-grader flipping away the note, which stated "I'm tired of school" and warned of a bomb, said Det. Lt. Robert Edwards of the First Precinct.
"You have a couple hours," he said the note read. "You'll never find the bomb."
Dunlap was arrested after "spontaneously" admitting to officers, "OK, I wrote it. This place does nothing about nothing," the complaint said.
After school officials reviewed surveillance footage, the teenager was called to the principal's office and held for police, said Bob Clifford, spokesman for the Suffolk district attorney.
She faces 11/3 to 4 years in prison if convicted, he said.
"She's mad at the school," Edwards said. "She really has no intent or capability to make a bomb."
Dunlap's legal aid attorney could not be reached for comment.
Amityville District Superintendent John Williams issued a statement saying safety is a top priority and that the student has been suspending pending the outcome of a superintendent's hearing.