Of the nine people injured, one is in critical condition, and two have been released, he said.
One woman died at the scene, and another died at a hospital, authorities said.
"Don't lose sight of the fact that these two individuals had a vision, had a name, had a future," said Col. Michael Edmonson of the Louisiana State Police. "It wasn't to die as they did horribly in this theater here."
John R. Houser, 59, was the gunman in Thursday's shooting, Craft said.
Houser was formerly of Alabama, and was "kind of a drifter" who is believed to have been in Lafayette since early July. He had been staying at a local hotel, Craft said.
Murder-suicides leave a mountain of unanswered questions. When the killer pulls the trigger on his victims and then himself, he takes with him to the grave the reasons that compelled the act.
So, while investigators won't be able to question the 58-year-old shooter who opened fire inside an auditorium at the Grand Theatre 16, that doesn't mean they won't painstakingly pore over his digital footprint, talk to his family and friends, and retrace his movements to answer the burning question: Why?
The onslaught of bullets at the multiplex in Lafayette on Thursday night killed two people and wounded nine before the gunman turned his handgun on himself.
"It does appear that it was random," said Sgt. Brooks David with the Louisiana State Patrol. "It wasn't that anyone in particular was picked out ... it just looked like it was a random shooting inside the theater."
David said they do know who the gunman is and where he lives. Finding out more could be tricky.
"They're going to have to move very carefully," said CNN legal analyst Alex Ferrer, a former police officer, attorney and judge.
In the Aurora, Colorado, theater shooting three years ago that killed 12 people and wounded 70 others, shooter James Holmes booby trapped his apartment. It was rigged to explode.
"It's always a possibility. That's why we don't want to release any names yet," David said.
"Hopefully when our agents get there, they will be able to clear that scene and talk to family and friends and find out why he may have done such a thing."
The shooter's name could be made public sometime on Friday, according to David.
Electronic devices also will be key to the investigation, according to Ferrer.
"The cell phone and the computer are going to be priceless," he said. Authorities can use software to recover the gunman's text messages and emails, even if they've been deleted. They can also track what websites he frequented.
The investigation will be thorough, even though the case will never go to trial because the shooter is dead. Police will build a complete profile on him, according to CNN legal analyst Sunny Hostin.
"He does have a criminal history," Lafayette Police Chief Jim Craft said. "It looks like it's pretty old -- nothing recent that we've found thus far."
Police don't think there was an accomplice.
"He appeared to be by himself," Craft said.
Sat quietly in the theater
Early evidence suggests the gunman bought a ticket for the movie "Trainwreck," went inside the theater and sometime during the film started shooting, David said. He didn't move from one theater to another.
The events of the evening left the police chief shaking his head.
"Why would a guy come into a theater in this city -- we have a relatively safe city -- and just randomly start shooting?" Craft said. "It's hard to figure out. He's deceased so we may now never know."