Shelby is one of only a few female officers to be charged in a fatal shooting in the past decade. If convicted, she faces a minimum of four years in prison.
Police cameras captured Crutcher walking towards his car with his hands above his head while officers followed closely behind with their weapons raised, the Washington Post reported. He was standing next to his SUV, his body facing the window on the driver's side, when he fell to the ground. The footage does not provide a clear view of when Shelby fired a shot.
Tulsa police say Crutcher did not have a gun on him or in his vehicle.
Benjamin Crump, an attorney for Crutcher's family, earlier said Shelby "must be held accountable for her actions".
In the 60 Minutes segment, Shelby said that moments before she fired, Crutcher looked back at her as if he was trying to assess his next move. She also believed that Crutcher may have been under the influence of a drug. An autopsy later showed that a hallucinogenic drug called phencyclidine, or PCP, was in his system.
"His shoulders drop, his arms drop, and he's reaching in and it's fast," Shelby said. "Just that would tell any officer that that man is going for a weapon."
Her attorney, Scott Wood, told the Tulsa World in September that Crutcher ignored commands to stop reaching into his pocket.
"I say with a louder, more intent voice, 'Stop! Stop! Stop!'" Shelby told CBS. "And he didn't. And that's when I took aim."
Crutcher's sister, Tiffany, told CBS that her brother did what he was supposed to do.
"Put your hands in the air and put your hands on the car," Tiffany Crutcher said. "And my brother did what my father taught us."
Prosecutors charged Shelby a few days after Crutcher's death. She has been out on bond awaiting her May trial.
The shooting drew national attention and comments from Donald Trump, who was a presidential candidate at the time.
Trump said the video left him feeling "very, very troubled". He also questioned why Shelby did what she did.
"That man went to the car, hands up, put his hand on the car. I mean, to me, it looked like he did everything he's supposed to do," Trump told a crowd during a September visit to a church in Cleveland Heights, Ohio. "And this young officer, I don't know what she was thinking. I don't know what she was thinking. Did she get scared? Was she choking? What happened? Maybe people like that, people that choke, people that do that, they can't be doing what they're doing."
In an interview with CNN, Crutcher's mother, Leanna, called her son a "compassionate" man.
"No one could ever do anything that would turn him away from being their friend," Leanna Crutcher said. "He loved people."
Shelby worked at the Tulsa Sheriff's Department from 2007 to 2011 before joining the police department.
Peter Holley, Katie Zezima and Kimberly Kindy contributed to this report.