The police chief told WSB-TV reporter Mike Petchenik that calling it a criminal investigation does not mean it will result in criminal charges and investigators will follow evidence wherever it takes them.
Brown was found face down in a bathtub at her Roswell townhouse more than a week ago. She has since been in a medically-induced coma.
Her father, Bobby Brown, denies reports that she is brain-dead.
Monday night, hundreds of fans and supporters held a candlelight vigil.
"Shining a Light for Healing for Bobbi Kristina Brown" was held at the Riverdale Town Center amphitheater south of Atlanta, a venue that Brown's father, singer Bobby Brown, christened as its first performer in 2010, said event organizer Corey Punzi, the city's marketing specialist.
Bobbi Brown is the only child between Bobby Brown and Houston. Her relatives have said she is "fighting for her life" at an Atlanta hospital.
Police, citing an ongoing investigation, have not disclosed many details of the circumstances in which Brown was found. Houston was also found unresponsive in a bathtub on Feb. 11, 2012, and later died.
Riverdale Mayor Evelyn Wynn-Dixon was among those who sang gospel hymns on stage, as members of the crowd sang and danced along.
Several vigil speakers touched on the struggles and scrutiny Brown's family has faced in recent years, comparing them to their own trials and tribulations. "They bleed and hurt like us," Wynn-Dixon told the crowd before singing the gospel song "There's a leak in this old building."
Brian and Poco Reese, both 52, of Johns Creek, Georgia, said they would make the roughly 40-mile drive back home feeling refreshed, uplifted and hopeful for Bobbi Kristina's recovery.
"We just continue to pray that the Lord does his will and whatever that may be for Bobbi Kristina's life on Earth, we don't know that," Brian Reese said. "We watched her grow over the years. We love her," Poco Reese added. "You know, with everything she's gone through, with everything she's endured, we love her even more."