Marcel Johnson, 21, is currently held on possession of paraphernalia charges.
He is also being questioned in the deaths of 22-year-old Ebony Talley and her 4-year-old daughter R'mani Rankins.
His connection to the case is unclear but, when asked, Johnson told Action News that he wasn't responsible for killing Talley and Rankins.
"I didn't do it," he said.
Police say both mother and daughter were stabbed to death. Their bodies were found around 3:30 p.m. Monday at the Avalon Court Apartments in the 3500 block of Oxford Valley Road following a fire.
Investigators believe that fire was set to cover up the crime.
"She was a good person. She didn't deserve this and her daughter, definitely, did not deserve this," cousin Dani Hodges said.
Family members say Talley, who was 7 months pregnant, was stabbed multiple times. Her daughter was stabbed once and suffered burns over 70% of her body.
Police say Johnson was found in the parking lot of an apartment complex with plastic bags commonly used for illegal drugs.
Johnson was charged with possession of paraphernalia and bail was set at 10% of $50,000.
Family members say there was a particular love interest in Ebony Talley's life recently.
Hodges told Action News she would not comment on that.
Relatives cannot understand why the killer would harm an innocent baby.
"Why kill an innocent baby? Why? Why? And to know that she was 7-months pregnant and to do that?" Hodges said.
The Red Cross was assisting 6 people who were affected by the fire, which occurred in the apartment of Ebony Talley's friend.