The family also criticised the state’s top prosecutor for the failure to bring charges against the officers.
A diverse group, including Ms Taylor’s mother, marched through Louisville on Friday evening. The demonstrations were peaceful, though at one point, police in riot gear fired flash bang devices to turn back a crowd on a street and authorities said two people were arrested.
About a dozen people who were out past the city’s curfew were arrested later.
Meanwhile, Oregon Governor Kate Brown declared a state of emergency as she announced that state troopers and sheriff’s deputies would be sent to Portland through the weekend.
The support is being sent to help police, in the state’s largest city, monitor a weekend rally by the right-wing group Proud Boys and counter protests by liberal groups.
Portland has been roiled by often violent demonstrations for more than three months following the police killing of George Floyd in Minneapolis.
Earlier, Ms Taylor’s lawyers and family expressed dismay that no one has been held accountable for her death.
“I am an angry Black woman. I am not angry for the reasons that you would like me to be. But angry because our Black women keep dying at the hands of police officers — and Black men,” Taylor’s mother, Tamika Palmer, wrote in a statement read by a relative.
State Attorney General Daniel 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.