It's been suggested Bobbi Kristina had suspicious injuries when she was discovered at her home last weekend.
The 21-year-old remains on a life support machine in hospital in Atlanta.
According to Yahoo News, the police investigation is targeted at Nick Gordon, Brown's boyfriend, who along with his friend Max Lomas reportedly discovered Bobbi Kristina face-down in the bathtub at her Atlanta home.
Brown's relationship with Gordon has been subject to both family and public scrutiny. Not long after Houston's death in 2012, Brown revealed she was romantically involved with the young man her mother had taken in about 10 years earlier. Gordon had lived with the family since he was 12 years old, but Houston never officially adopted him — a fact Bobbi Kristina pointed to in defending their relationship on social media.
But not all of Brown's family members were convinced by this rationale. In an interview with Oprah Winfrey last year, Whitney's sister-in-law, Marion 'Pat' Houston, admitted the relationship 'just didn't sit right with me.'
"I always looked at them as being, you know, the brother-and-sister type, Houston said. I just did not see the relationship moving in that direction."
As the only child of Whitney Houston and her ex-husband, singer Bobby Brown, Bobbi Kristina is her mother's sole heir, which might explain why some family members seem to be pre-emptively countering any attempt Gordon might make to claim Whitney's fortune.
Despite their wearing rings and referring to each other as husband and wife in public and on social media, Bobby Brown's lawyer said, in a statement to ABC News this week, that "Bobbi Kristina is not and has never been married to Nick Gordon."