The brother and sister, arrested as accomplices in the fatal shooting of a Nashville, Ark., woman, have become “persons of interest” in a 35-year-old murder investigation in Texarkana, Texas, authorities said Thursday.

JoAnn Hicks, 74, of Ogden, Ark., along with her brother, David Camp, 63, of Stamps, Ark., were arrested Tuesday and charged as accomplices to first-degree murder. The siblings are accused in helping plan the murder of David Camp’s estranged wife, Robin Camp, 42, in the Family Dollar Store May 26 in Nashville.

The investigation took a strange twist when la...