An elderly woman was battered and killed inside her apartment in a Brooklyn housing project, police said Thursday.

Jacolia James, 83, was found unconscious by a family member inside her apartment in the Carter G. Woodson Houses on Powell Street near Dumont Avenue in Brownsville on Tuesday night, cops said.

Police and medics responded and declared James dead at the scene, cops said. She had a wound on her head and trauma to the body when she was found, authorities said.

Investigators are now working to find out how she was killed and to identify possible suspects in the slaying, police said.

No arrests had been made by Thursday evening, cops said.