An amended lawsuit claims Nick gave Bobbi a "lethal cocktail" and then put her face down in cold water.
Bobbi's family have accused Nick of "wrongly death", adding the claims to an original lawsuit filed on June 24 against the tragic star's partner.
The lawsuit, filed in Fulton County Superior Court, Atlanta, accuses Nick of assault, battery, intentional infliction of emotional distress, and transferring money from Bobbi Kristina's account into his own without permission.
Bobbi, the daughter of singers Whitney Houston and Bobby Brown, died last month at the age of 22.
Her death came six months after being found unconscious in her bath at her home in Roswell.
The family's lawsuit, seen by NBC's 11 Alive, claims that Nick "gave Bobbi Kristina a toxic cocktail rendering her unconscious and then put her face down in a tub of cold water causing her to suffer brain damage".
The incident is said to have happened after a row.
Bobbi was reportedly found face down in the bath 'with a tooth hanging loose' from her mouth.
She was taken to hospital and put in a medically-induced coma, but tragically never regained consciousness.
No criminal charges have been filed against Nick.
He has denied the claims in a statement which reads: "Nick has been heartbroken and destroyed over the loss of his love and it's shameful that such baseless allegations have been presented publicly."
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