And the family's attorney said Friday he is counting on a different, federal investigation for justice.
"We hope the FBI investigation finally gets justice for Bre and her family," attorney Benjamin Crump tweeted.
Protests erupted in Louisville and across the country after Attorney General Daniel Cameron announced Wednesday that a grand jury did not charge three officers directly with Taylor's death, more than six months after police shot her in her home while executing a search warrant.
The grand jury indicted one officer on first-degree wanton endangerment charges, accusing him of blindly firing shots that penetrated the walls of a neighbor's apartment.
The FBI has said it is investigating Taylor's death.
Crump has called for Cameron to release the transcripts of the grand jury proceedings.
Grand jury proceedings are generally kept secret to encourage witnesses' and jurors' candor, prosecutors and legal experts say. Exceptions have included the release of grand jury proceedings in the Michael Brown case in Ferguson, Missouri.
Taylor's family is "heartbroken" and "outraged," Crump said Thursday.
"They were baffled by what Kentucky Attorney General David Cameron actually presented to the grand jury. Did he present any evidence at all on behalf of Breonna Taylor?" Crump said to CNN's Anderson Cooper on Thursday.
"We do believe (the investigations into Taylor's death) was a coverup from go," Crump said. "They always intended to sweep this under the rug as if Breonna Taylor's life didn't matter."
Kentucky Gov. Andy Beshear, Louisville Mayor Greg Fischer, and former Kentucky Assistant Attorney General John W. Stewart also have called for the grand jury transcripts to be released.
"If these two officers did not get indicted, then the grand jury testimony ought to be public. You can't hide behind the secrecy of the grand jury," Stewart told CNN Thursday.
Fischer said Thursday the city was working with the attorney general's office and the FBI to determine what information could be released without interfering with ongoing investigations.
Louisville's mayor is extending the city's curfew
After another night of protests Thursday, Louisville's mayor said he is extending the city's curfew through the weekend to balance people's "rights to peacefully protest with the duty to protect public safety."
The 9 p.m. curfew would keep protesters, first responders and bystanders safe since most of the violence has happened overnight, Fischer said, while allowing demonstrators "to voice their calls for racial justice and equity during the day."
On Thursday night, after a nearly two-hour peaceful standoff between the Louisville Metro Police Department officers and protesters on church property, police moved out to allow protestors to go home.
As demonstrators stepped off grounds of the First Unitarian Church property, one of the protestors advised the group that if they didn't leave and go to their cars, they would be arrested.
The curfew will not apply to people commuting to work, houses of worship for services, or seeking me
