Sgt. Vic Regaldo said the driver couldn't see the girl and likely couldn't have prevented the accident.
The driver will not be ticketed.
In a statement, Tulsa Public Schools Superintendent Keith Ballard spoke of the district's "deep sorrow" at the loss of the young girl.
"Our hearts and prayers also go out to the driver and family of the vehicle, as this was an unfortunate accident. While we believe there is little that could have been done to prevent this tragedy, we want to urge drivers to be cautious when driving near schools and crosswalks," he said. "They need to give their full attention to the road and be mindful of children and their surroundings at all times."
On Wednesday, Tulsa Publics Schools campus police stationed an officer outside the school to help direct traffic.
School officials say they will provide an officer for the next several days to help reassure teachers, students and parents.
Many parents told 2News they like the officer being there.
A grandparent of a first and third grader escorted her grandchildren over to a makeshift memorial where they left their condolences.
Doris Taylor says while the accident is a horrible tragedy, it can serve as an important reminder about pedestrian safety, especially for kids.
A fund to help Halstead's family pay for funeral expenses has been set up.
Anyone who would like to donate can visit any RCB Bank and ask to contribute to the Emmalee Rose Memorial Fund.