Lawyers for the family called on him to release the transcripts of grand jury proceedings while vowing to continue protests until the officers are charged.
Tamika Palmer, Ms Taylor’s mother, said in a statement read by a relative to a gathering in Louisville that she did not expect justice from state Attorney General Daniel Cameron.
Ben Crump, a lawyer for the family, urged the prosecutor to make the transcripts public, so people can see if anyone was present at the grand jury proceedings to give a voice for Ms Taylor.
Governor Andy Beshear, a Democrat, has also called for Mr Cameron to release what evidence he can.
Mr Cameron’s spokeswoman Elizabeth Kuhn said the prosecutor understood that Ms Taylor’s family “is in an incredible amount of pain and anguish” and that the grand jury decision was not the one they wanted.
But, the statement added, “prosecutors and grand jury members are bound by the facts and by the law”.
Ms Taylor, a black woman who was an emergency medical worker, was shot multiple times by white officers after her boyfriend fired at them, authorities said.
He said he fired in self-defence, wounding one officer. Police were conducting a drugs investigation and entered on a warrant connected to a suspect who did not live there, and no drugs were found inside.
Mr Cameron has said the investigation showed officers acted in self-defence. The grand jury charged one officer, who has already been fired, with firing into a neighbouring apartment.
At almost the same time that Ms Taylor’s family was decrying the handling of her case, a man accused of shooting at police during protests on Wednesday was being arraigned. Two officers were wounded and expected to recover.
A not guilty plea was entered on Friday for Larynzo D Johnson, 26. Bond was set at 1 million dollars.
Zac Meihaus, the attorney representing Johnson at the arraignment, said it is difficult to “pinpoint” if Johnson fired the shots in question.
A prosecutor replied that a gun was recovered from Johnson, and there are video and witness accounts of the shootings.
The big question for Louisville, which has been torn apart by Ms Taylor’s death, and the larger issue of racism in America was how to move forward.
The FBI is still investigating whether Ms Taylor’s civil rights were violated, and some have put their hope in that probe but the burden of proof for such cases is very high.
Many have taken to the streets around the country.
On Thursday, some of them raised their fists and called out “Black lives matter!”
Others tended to the letters, flowers and signs grouped together in a square in downtown Louisville. All of them said her name, which has become a rallying cry.