It would seem the prudent thing to do is some investigation. Check with the police depratment and Sheriff's department in the city and county where the mother reides to determine if there have been any police calls to the home. If there have been, pull a report. Check the b/f's criminal and drivinhg record if you can.
You will need more than the naked assertion of a child. You may even wish to raise your concerns to the other parent and seek her input before jumping to a conclusion.