Brown, 21, was placed in a medically induced coma and the status of her brain function won't be known until the sedatives are reduced, the source told CNN.
"It is going to be a waiting game," said the source.
Brown "was not breathing" when a man identified as her husband found her Saturday morning inside her townhouse in the Atlanta suburb of Roswell, Georgia.
He called 911 and performed CPR until public safety officers arrived and took over, said police spokeswoman Lisa Holland.
The spokeswoman said when Brown was found, she was "unresponsive, meaning not breathing, no heartbeat."
In scanner traffic, emergency services could be heard describing an "ECHO-level response" -- urgent and life threatening -- with "possible cardiac arrest."
"Twenty-one-year-old female in the bathtub, facedown. PD's (police department's) en route."
Brown was taken to a local hospital, where "she is still alive and breathing. Other than that, I don't know her condition," Holland said Saturday.
Nobody knows what caused Brown's unresponsiveness, Holland said, but police consider it a medical incident at this time. She said investigators had found nothing to indicate it was drug- or alcohol-related.
Police had been to the residence recently. Somebody reported a fight there January 23, but nobody answered the door and officers found no evidence of an altercation, Holland said.
The police spokeswoman noted one oddity in the case: "Her mother died in the very same manner."
Three years ago, Houston was found dead in a bathtub at the Beverly Hilton on February 11, hours before she was to attend a pre-Grammys bash.
An autopsy later revealed
that she'd drowned facedown in "extremely hot water" about 12 inches deep. The Los Angeles County coroner ruled it an accidental drowning with the "effects of atherosclerotic heart disease and cocaine use" as contributing factors.
Brown is her only child.
"She encourages me and inspires me," Houston once said of her daughter. "When I look at her eyes and I see myself, I go, 'OK. I can do this. I can do this.'"
Daughter of acclaimed singer, R&B standout
Brown was born in 1993 during Houston's marriage to R&B singer Bobby Brown, which ended in divorce in 2007.
The daughter of music royalty became a public figure during the mid-2000s reality show "Being Bobby Brown," in which she frequently appeared alongside her parents and often had a front-row seat to their marital fireworks.
Bobby Brown requested privacy in a statement issued Sunday by his lawyer, who said that Brown was at the hospital with his daughter.
"Please allow for my family to deal with this matter and give my daughter the love and support she needs at this time," Bobby Brown said.
Mother and daughter performed together on national TV in 2009, when the two sang "My Love Is Your Love" in Central Park on ABC's "Good Morning America."
Given the pair's close relationship, it's no surprise that Houston's death was a major blow.
Days after her mother's body was found, a grieving Bobbi Kristina -- then 18 -- was taken to Cedars-Sinai Medical Center because she was "overwhelmed," family friend Kim Burrell said.
"She loves hard," Burrell said then of Bobbi Kristina. "She's going to be OK, and we're going to see to it."
Married a man who was taken in by Houston
Brown appeared on episodes of Lifetime's brief reality show "The Houstons: On Our Own," which followed her life after Houston's death.
One of that reality show's storylines revolved around Brown's relationship with Nick Gordon, who lived with Houston and her daughter from the age of 12.
And in January 2014, she tweeted out a picture of wedding rings, presumably belonging to her and Gordon, along with the words, #HappilyMarried• SO#Inlove."
"(Houston) made me promise several times to look after Krissy ... and, Mom, I will never ever, ever break that promise," Gordon told the entertainment show "Extra
" afterward, saying Houston "just treated me like she gave birth to me."
It was unclear whether Gordon came home Saturday morning to find his wife in the bathtub or had been in another part of the house overnight, Holland said.
Police have obtained a search warrant to look through the house, but that's standard procedure, she said.
Concern for Brown surged again after news broke.
Music director Michael Bearden
sent along "healing energy to the daughter of a late great friend." Songwriter Diane Warren tweeted
, "I hope Bobbi Kristina gets the help she needs."
"Poor thing," Warren wrote. "Almost 3 yrs to the day her mom passed and the same thing almost happened to her."