The Louisville police officers had been granted a "no-knock" warrant that allowed them to enter the property without warning, although police said they had knocked and announced themselves at Ms Taylor's door.
The officers, who had not activated their body cameras as required, shot Taylor multiple times, killing her.
"If it is needed, we will authorize it", Beshear said at a news conference.
Federal buildings have begun to close and a state of emergency was declared Tuesday morning in Louisville, possibly in anticipation of protests and fears of looting.
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On Tuesday, 478 were recorded in the province, with 425 new cases reported the previous day. No person was listed as hospitalized nor are any people in intensive care.
The case exposed the wide gulf between public opinion on justice for those who kill Black Americans, and the laws under which those officers are charged, which regularly favor working police and do not often result in steep criminal accusations.
Kentucky Attorney General Daniel Cameron, a Black Republican, has said his investigation into Taylor's death is ongoing, but has declined to confirm media reports that he is convening a grand jury to vote on whether to bring criminal charges against the officers.
Police secured the warrant on the grounds that they believed Taylor's ex-boyfriend Jamarcus Glover was keeping drugs and money in her apartment, but they found neither.
Mr Walker was initially charged with attempted murder and assault of a police officer, but the case against him was dropped in May amid national scrutiny of the case.
Protesters across the United States have demanded justice for Ms Taylor and other black people killed by police in recent months. It's enormously ironic that the accused drug dealer here acted with honor, refusing to falsely discredit Bre after her death - even when offered the temptation of no prison time for lying, while prosecutors and police acted in the most egregiously dishonest and dishonorable way possible.
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The benchmark FTSE Bursa Malaysia KLCI Index extended declines after Anwar's announcement to slide 0.6% to 1,496.48, the lowest close since Sept 10.
Meanwhile, a Louisville judge ruled on Monday that police do not have to release the investigative file into the fatal police shooting of Taylor since doing so would harm the integrity of the case, which is still ongoing.
An undated photo provided by the Taylor family's attorney shows Breonna Taylor in Louisville, Ky.
In the leadup to Wednesday's announcement, legal experts said homicide charges were unlikely because the officers could invoke self-defence after Walker fired a shot. Breonna Taylor should still be with us and her family deserved justice today. (AP Photo/Ted S. Warren) (AP/AAP) A protester confronts police during a rally in downtown Lexington, Kentucky, against the deaths of George Floyd and Breonna Taylor.
Last week, the city of Louisville settled a lawsuit from Taylor's family for $12 million and pledged several police reforms as part of the agreement.
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Depuis ce mercredi soir, la métropole de Toulouse est classée en " zone d'alerte renforcée " par le ministère de la Santé. Le taux de positivité est de 9,9 % dans la capitale pour la semaine du 13 au 19 septembre, avoisinant le seuil d'alerte .