Taylor (26) was killed on March 13 when Police forced entry into the home. She was a black hospital worker, and was shot six times as three officers raided her home.
Protesters took to the streets in several US cities after the court announcement. Protests also took place in New York, Washington, Atlanta, and Chicago according to foreign media.
A grand jury in the city of Louisville returned only one minor charge against one of the officers.
The attorney general said that the action of the two other officers' had been justified.
A state of emergency has been declared and the National Guard have been deployed. A three-day curfew from 21:00 to 06:30 has been introduced.
Meanwhile, officials in Louisville, Kentucky agreed to pay $12m (£9.3m) to the family of Breonna Taylor.
Former Vice President and Democratic presidential nominee Joe Biden has tweeted his thoughts on the protests and the shooting of two police officers in Louisville:
"Even amidst the profound grief & anger today's decision generated, violence is never & can never be the answer. Those who engage in it must be held accountable. Jill & I are keeping the officers shot tonight in Louisville in our prayers. We wish them both a swift & full recovery."