Oliver initially claimed the vehicle, driven by one of Edwards' brothers, had reversed into the officers, justifying his decision to open fire on the Chevy Impala.
In May, Oliver was sacked and then arrested after the Balch Springs Police Chief said body camera video did not match his version of events in the Edwards shooting.
At the time of Oliver's arrest, a spokeswoman for the Dallas County Sheriff's Department said the arrest warrant was issued because evidence suggested Oliver "intended to cause serious bodily injury and commit an act clearly unsafe to human life that caused the death of an individual".
Oliver was also charged with four counts of aggravated assault, for the four other teenagers in the auto with Edwards when Oliver shot a rifle into the vehicle as it drove away from a party on April 29.
"We have some great police officers", she said.
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If convicted, he would be the first police officer convicted of murder in Dallas county since 1973, the report adds.
Oliver, who first joined the Balch Springs police in 2011, was sacked shortly after the fatal shooting this past April.
Haber later said the body camera footage showed the auto was driving forward - away from the officers, not reversing towards them.
A former Balch Springs Police officer has been indicted by a Dallas Grand Jury for murder in the death of a teenager.
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"It is important to let our community know that justice is proceeding effectively and thoroughly at the Dallas County DA's Office", DA Johnson said.
In late June, Oliver was indicted on two counts of aggravated assault involving a separate case that occurred before the Edwards shooting. "If you do wrong, we will prosecute you".
In the Edwards' case, Oliver faces up to life in prison.
Oliver later turned himself in to the Parker County Jail on a $300,000 bond.
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