Aberdeen Police Chief Carl Colasacco said they don't see these kinds of child-abuse cases in their town, especially those that lead to the death of a young child.
"It's very sad," he told ABC11.
Ashley Ann Vinesett, 34, and Cody Jerome Davis, 34, are in Moore County custody Tuesday.
Davis faces a first-degree murder charge, a charge of felony child abuse severe bodily injury and a charge of possession of stolen goods and property. Vinesett is charged with felony child abuse severe bodily injury to her daughter.
Police said the Spartanburg, South Carolina, couple was staying at the Super 8 motel in Aberdeen when they rushed the girl to First Health Moore Regional Hospital on Monday morning.
She died in the emergency room soon after staffers notified police of her condition.
Authorities said a preliminary autopsy led to the arrest of the couple later Monday afternoon. Colasacco said the report indicated that the young girl's death was by homicide.
"All my men and women got children and it's hard to deal with a small child's death," Colasacco said, "especially in a case that this was, in the manner that this was. The guys are still working out and the ladies are still working hard today trying to close up some small ends of it, find out some final pieces of the puzzle"
Colasacco would not confirm the cause of death Tuesday, saying he would wait until an official autopsy is completed.
He said the couple potentially faces additional charges.
Vinsett is being held on a $500,000 secured bond. Davis is being held on no bond.
Their first court date is scheduled for Thursday, according to jail records.