Firefighters put out a blaze in the Vivian Drive home in a rear bedroom and crawl space, Morgan said.
The fires have caused more than $10,000 in damage to the home, Morgan said.
The state fire marshal's office is investigating the two fires, Morgan said.
The two fires were put out quickly and no one was injured, Morgan said.
Fire investigators were interviewing neighbors in the Camelot subdivision located in the south end of Berkeley County to determine if they had seen anything suspicious, Morgan said.
On March 7, Erika Birdsall's nude body was found stuffed inside a sleeper sofa behind the H-Mart convenience store.
A passerby discovered her when he thought about taking the sofa to a friend.
An autopsy later determined she had died of multiple stab wounds.
The home has been unoccupied since the March 14 arrest of Clyde Birdsall, Erika Birdsall's husband, on an unrelated federal weapons charge of being a convicted felon in possession of a weapon.
Birdsall is being held without bond at the Eastern Regional Jail awaiting trial on the weapons charge in federal court.
Although he has not been charged in the slaying, U.S. Magistrate David Core has said Birdsall is a suspect in the death of his wife.
His arrest came when investigators conducted a search of the home and found him there with firearms.
Police also seized blood and other evidence and a crime lab is analyzing it to determine if Erika Birdsall had been killed at the home.
Berkeley County Prosecuting Attorney Pamela Games-Neely said Sunday night it still has not been determined if she was killed in the house.
She said she was out of town during the weekend and had not heard about the two fires at the Birdsall home.