Tillery is charged with murdering Air Force Sgt. Albert Adams three years ago in Cumberland County. Tillery was allegedly having an affair with Adams' wife.
The defense is focusing on the testimony of a former Cumberland County sheriff's lieutenant. He told a military court that investigators failed to follow up on some leads, which include not tracking down a man who told a pawn shop owner he had information about the murder.
Prosecutors allege that Tillery rented a green Dodge Stratus in Atlanta, then drove to Fayetteville and killed Adams.
A North Carolina judge dismissed state charges against Tillery last year, citing a lack of evidence, but a military judge says there is enough evidence to try him.
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