Criminal minds: Inside the head of a man authorities believe to be a killer

Donnie Brantley may have been incredibly smart -- or incredibly stupid. If he did kill his wife Marsha in 2009, he would be one of the most bumbling criminals in Tennessee history. He also may be one of the hardest to convict. 

What makes this case so tough for prosecutors, lies in what Brantley said, what he did – and what he didn't do.

First, investigators say Brantley lied repeatedly about where and why Marsha had gone. He said she'd left him to go to Florida, and that she'd gone out west. He also claimed she'd just gone camping nearby. She never turned up anywhere and never left any sort of paper trail to back up any of her husband's stories.   

Second, investigators say he lied about some of her most important belongings. He told police Marsha had taken her phone – but police easily obtained phone records showing the phone never left the area of the Brantleys' house, and even suggesting Donnie himself was using it. He told investigators Marsha had left her car at a local Walmart where she worked. The first time they checked, it wasn't there. The next time it was. Either way, the Walmart manager had never heard of Marsha Brantley.

Then there was Brantley's strange behavior.  

He never reported his wife missing. Her family says he never tried to help them find her. Just hours after investigators first approached him, he pawned some of Marsha's jewelry. Investigators later found the remainder of her things in garbage bags in the house.    

But if Donnie Brantley did murder Marsha – prosecutors have struggled to say how, when, where - and they can only speculate about why. That's because there is one critical thing investigators did not find - any physical evidence of a crime. 

There's no blood, no fingerprints, no gunshot residue, no DNA and no murder weapon. Forensics experts tell 48 Hours that's not easy. In fact, even seasoned criminals rarely manage to get away totally clean.

But the most important missing evidence in the Marsha Brantley murder case is Marsha Brantley herself. Winning murder trials without a dead body in evidence is difficult, but far from impossible. Prosecutors maintain Donnie Brantley's statements and behavior are the building blocks of a rock solid circumstantial case.

"48 Hours" was there as the case went to court.  And we were shocked by what happened next.

"48 Hours" producer Josh Yager investigated the disappearance of Marsha Brantley and the case against her husband Donnie Brantley for the episode, "Missing Marsha," which airs Saturday, June 29 at 9/8c on CBS.