Lynn Giovanni, 45, was charged with murder and was being held at a psychiatric hospital on $250,000 bail. Authorities would not comment on a possible motive.
Several hours after Sunday's slaying, the mother tried to kill herself by crashing her car into a guardrail along a highway in a nearby town, authorities said. She sustained only minor injuries.
State police investigating the accident questioned Giovanni, who told them "of a possible homicide," said Union County Prosecutor Theodore Romankow.
Police then broke into the house where Giovanni had been staying with her mother and daughter, and found the bloodied body of Nicole Giovanni.
The girl was a freshman at Roselle Catholic High School, where administrators described her as popular and an accomplished indoor track runner. Grief counselors were called to the school Monday.
An arraignment was tentatively set for Wednesday.