On Sunday, officers responded about 6:45 p.m. to the 900 block of Maple Street in reference to a reported shooting.
They found two people with gunshot wounds: Teresa Davis, 63, and her son, Joseph Jeffreys Jr., 26. Both were pronounced dead at the scene.
Michael Sharron Wright, 41, was taken into custody by the Granville County Sheriff's Office. He is being held without bond at the Granville County Detention Center.
This is still an active investigation, authorities said.
Stay on top of breaking news stories with the ABC11 News App