The 21 year old has been in a medically-induced coma following her hospitalisation on 31 January (15), when she was found unresponsive and face down in a bathtub at the Roswell, Georgia home she shares with her partner Nick Gordon.
She underwent the surgery on her windpipe on Wednesday (18Feb15), but her condition remains unchanged.
A family source tells People.com, "The tracheotomy is a different place for the tube to go. Everything else remains the same. It's a waiting game. The family is hoping and waiting.
"It's a normal procedure to have the tracheotomy because if you have a breathing tube down there for a long time, it can cause an infection."
The insider adds, "She is still critical and we don't know what the outcome will be. No one is giving up on this kid."
Brown's family members, including father Bobby Brown and grandmother Cissy Houston, have been holding a bedside vigil for the youngster ever since her hospitalisation.
The tracheotomy was performed two days after a lawyer for singer Bobby Brown dismissed "false" reports suggesting his daughter would be taken off life support this week (begs16Feb15).
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