According to the BBC, the Basirhat police station yesterday sent the woman for medical examination.
The woman along with her husband and two daughters were crossing the Khojadamga border of Bangladesh to Kolkata for treatment.
The 122 battalion of the BSF patrolling the Ichhamoti Bridge intercepted and detained the family.
Some BSF men then reportedly raped her and threatened to kill her husband and children if she resisted.
Circle Inspector of the Basirhat station Ziadur Rahman told the BBC over telephone that a case had been filed and that the no BSF personnel had been identified yet.