However, Brett Hankison was charged with gratuitous endangerment for allegedly shooting a nearby apartment.
The response infuriated activists who gathered in Louisville to protest the decision.
There were clashes with police, with video showing discarded bottles and a number of arrests.
Video footage also showed members of a heavily armed militia in Louisville, some of whom chanted “USA, USA”.
Previously, Mr. Trump was asked what his message to the American “black community” was following the Breonna Taylor decision.
He replied, “My message is that I love the black community.
READ MORE: Trump hints he won’t accept US election result if Biden wins
“It’s time to fundamentally reform our racist and broken criminal justice system, end qualified immunity and hold police officers accountable.”
Earlier in his press conference, Mr. Trump was asked if he would respect the November presidential election result if Democrat Joe Biden emerges as the winner.
The president has previously suggested, without providing any evidence, that Democratic activists attempt to rig the election using postal ballots.
Speaking to Mr. Trump, a reporter asked, “Are you going to commit to a peaceful transfer of power after the election?”
The President replied, “Well, we’ll have to see what happens. “
Earlier, Mr Trump had said he wanted his new Supreme Court nominee, replacing Justice Ruth Bader Ginsburg, in place ahead of the election if there was a contested outcome.
He said, “I think it’s better if you go before the election because I think this scam that Democrats are pulling is a scam, this scam will be in the United States Supreme Court.
In the event of a contested presidential election, the Supreme Court’s decision could prove decisive.
In 2000, he assigned the presidency to George W. Bush after ruling out a recount in Florida that could have benefited his Democratic rival Al Gore.
Justice Ginsburg, who died on September 18, was a leading Liberal member of the United States Supreme Court.