Jazmine was in a vehicle with her mother and three sisters when a man in a red or maroon pickup truck drove up and opened fire.
"All evidence gathered so far in the Jazmine Barnes Homicide case supports investigators; strong belief that she and her family were innocent victims", the Harris County Sheriff's Office tweeted early Sunday.
Investigators identified Black as a suspect based on a tip, discovered evidence that corroborated the tip and charged him with capital murder Saturday.
Based on a description from one of the occupants of the Barnes family vehicle, authorities had been searching for a white man, raising concerns the shooting was racially motivated.
The source told police that the suspects had mistaken the vehicle Jazmine was riding in for somebody else's and that it was shot at "by mistake".
Police now say they do not believe the family was targeted and that the shooting may have been a case of mistaken identity.
Officials said investigators are also looking into the possibility that others could be charged in the case.
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Jazmine was shot in the head and died at the scene.
"We're not going to rest until we find justice for Jazmine", Gonzales said.
Houston Mayor Sylvester Turner said the arrest "should serve as a warning to all violent offenders who prey on our community" that they will be arrested eventually.
Ms Washington, who was shot in the arm, tearfully recounted the attack from her hospital bed and urged the gunman to give himself up.
At about 7 a.m., a man drove up next to their auto and opened fire, Washington said.
They also chanted: "What do we want?" Jazmine's funeral is scheduled for Tuesday.
"Every time I see one of you all reach out for me, I can hold my head up".
S. Lee Merritt, an attorney advising the Barnes family, said the arrest "was welcome news to the family". DeAndre Hopkins, a wide receiver for the Houston Texans, announced on January 3 that he would be donating his $29,000 playoff game check to help Barnes's family cover funeral expenses.