The woman, however, was untraced amidst speculation that she had killed the two children, aged 5 and 2 years.
The incident occurred at Budhijhilwa village under Saraiyahat police station.
Police said the woman, Lalitha, was beating up the two children and she was resisted by her mother-in-law yesterday.
In a fit of rage following the incident, Lalitha burnt some documents and a box last evening and left home taking the two children.
Police said a search was on to find out Lalitha.