Harris continued to drive into a residential area toward his home before stopping.
When Harris got out of his car, officials say there was an "encounter" with Trooper Jermaine Saunders that prompted Saunders to fire his gun, issuing the fatal shot.
Residents who saw Harris after the shooting said they did not see a weapon on or near him, and the SBI confirmed Friday they had not recovered one.
Some residents in the neighborhood where the shooting happened think that Harris didn't stop right away because of his hearing impairment, WSOC-TV reported.
It's unclear whether Harris knew the trooper was trying to pull him over, or whether the trooper knew Harris was deaf.
The SBI said it is still collecting evidence from the scene, including video from the trooper's in-car cameras.
The Highway Patrol said Saunders is on administrative leave while the investigation is ongoing.
Harris' family raised money for his memorial and cremation on YouCaring.
"Any monies left over will be used to set up a foundation in his name to educate and provide law enforcement proper training on how to confront Deaf people," the fundraiser description says. "Subsequently, we hope to change the DMV registration system by requiring states to set up a 'DEAF' alert to appear when law enforcement look up a car's license plate. With this change, Daniel will be a hero in our Deaf community."
Friends and neighbors gathered Monday evening to honor Harris. Family members told the crowd at the vigil that they want answers.
Harris' brother, Sam Harris, said his brother was a family man with a big heart.
"He was effervescent, funny, social, people enjoyed being around him, just a very unique man," Sam Harris told WSOC via an interpreter. "It's a nice feeling that you've got a community like this that supports you. It can be overwhelming in a time of grief like this."
Sam Harris hopes the shooting spurs greater awareness between police and the deaf community.
"The police need to become aware of how to communicate with deaf people, what that might look like and how to avoid situations like this from ever happening again," he said.
Trooper Jermaine Saunders has retained an attorney and the SBI is waiting to interview him.