The fight broke out over the issue of sitting in the classroom of the school in Rampur Tola, Deputy Superintendent of Police Umeshwar Chaudhary told PTI from the school where he had gone to record statements.
According to preliminary information, two class I girls beat up their classmate Sita Kumari on Tuesday following a quarrel over sitting on the sack.
Sitting on sacks is the practice in the school where there is no bench or desk.
The DSP said when the girls were fighting, a teacher identified as Seema Kumari was present there but did not intervene.
Later, when Sita and her elder sister, a class IV student of the same school, were returning home, the two girls along with their mothers again attacked the two siblings.
They became unconscious and Sita died on the way to Sadar Hospital at Motihari where her sister has also been admitted in a critical condition, the DSP said.
An FIR has been registered against five persons — the two students, their mothers and teacher Seema Kumari, police said, adding no one has been arrested.