Is child custody document mandatory for accompanying kid (4 years old)

[flying_albatros]

My sister divorced her husband due to extremely violent behavior in 2017. He had records of threatening my sister and the whole family with a knife and gun. At that time, she ran away with her kid and divorced him later. After that, there was never a settlement regarding the custody of their child between them. He never filed a case, neither did she. Now, she is planning to pursue an MS/Ph.D. degree in the US.
My question is if she applies for an F1 visa with her child accompanying her, is it mandatory to show any sort of child custody papers? Please let me know any information that you know.