Kenneth Gleason, 23, was charged in connection with two killings that happened last week -- and with attempted murder in a separate incident.
The victims in the fatal shootings, 49-year-old Donald Smart and 59-year-old Bruce Cofield, were shot to death two days and a couple of miles apart, authorities said.
Investigators were able to match the suspect's DNA to shell casings recovered at two shooting scenes, authorities said.
The evidence was matched to Gleason while he was being held on charges related to the theft of a book, "The Hitchhiker's Guide to the Galaxy," East Baton Rouge District Attorney Hillar Moore III told reporters.
Authorities said the motive remained under investigation though they had described the shootings on Sunday as possibly being racially motivated. Gleason is white, the victims were black.
"It's an ongoing investigation. We're not completely closed off to that," Baton Rouge Police Sgt. L'Jean McKneely told reporters Tuesday.
"We're going to continue to talk to Mr. Gleason to see if we can get some addition information as to the reason why. So we're not going to speculate."
Jonathan Dunnam, interim Baton Rouge Police Chief, said Gleason may have struck again had he not been picked up.
"Baton Rouge has been through a lot of turmoil in the last year," Dunnam said.
"I think had there not been a swift conclusion to this case I feel confident that this killer would have probably killed again. He could have potentially created a tear in the fabric that hold this community together."
Moore said Gleason could face the death penalty in connection with the slayings. "He made statements but at this time I don't think it would be appropriate to say what he said," Moore said of the suspect.
Investigators said that in addition to the two homicides, Gleason -- who is white -- allegedly opened fire on the home of an African American family who live near his home.
Police said Monday that in both instances, the suspect shot the victim from a vehicle. After the victims fell, the shooter got out of the car, walked to the victims and fired several more shots.
Gleason was taken into custody on drug-related charges Saturday after police stopped a car matching the description of the vehicle used in the shootings.
He was released from jail Sunday after posting a $3,500 bond, Savannah Jones with the East Baton Rouge Sheriff's office told CNN. He was later rearrested for the theft of the book. It's unclear whether Gleason has an attorney.
Smart's body was found late Thursday on Alaska Street, around the corner from his home, police said. Cofield, who was believed to be homeless, was killed on Florida Street, about two miles to the north.