Raleigh, N.C. — A police detective testified Thursday that he believes Brad Cooper strangled his wife inside their Cary home in 2008 and dumped her body several miles away.

"I believe Nancy Cooper came home in the early-morning hours of July 12, and Mr. Cooper murdered her," detective Adam Dismukes said.

Brad Cooper, 37, was arrested in the case more than three months later and is standing trial for first-degree murder. He faces life in prison, if he's found guilty.

Defense attorneys say police ignored evidence in their investigation that could have helped them find her real killer or killers and focused only on proof to support their "Brad-did-it" theory.

Slideshow     Inside the Cooper house

Nancy Cooper, defense attorneys claim, left her house for a run on the morning of July 12, 2008, but never returned home.

A friend reported the 34-year-old missing later that day. Two days later, a man walking his dog found her lying facedown in a drainage ditch in an undeveloped subdivision off Fielding Drive, just outside Cary's town limits.

Dismukes said during cross-examination Thursday that several things inside the couple's house, including the front hallway, suggested the possibility that there had been a struggle when Nancy Cooper returned home from a party at a neighbor's house.

Now an undercover detective, Dismukes' testimony could not be posted on WRAL.com as a result of a ruling by Superior Court Judge Paul Gessner that certain witnesses not be recorded because of law enforcement concerns about ongoing and future criminal investigations.

Kurtz spent several hours going through dozens of photos taken of the Cooper home while the case was still a missing persons investigation and questioned Dismukes at length about why they made him think that Brad Cooper might have killed his wife.

Jessica Adam, a friend of Nancy Cooper, testified earlier this week that the photos showed that items were removed, moved or changed sometime between the afternoon of July 11, 2008 – when she had been at the house – and the next afternoon.

Decorative ducks that had been sitting on a credenza and bamboo sticks in a vase in the foyer were missing from one photo, signifying to Dismukes that a struggle possibly occurred there.

But Kurtz said other items in the hallway weren't damaged, including a lamp. He said there were no scuff marks on the floor and that police never searched for the missing items.

Other items in the home, Kurtz said, were also intact, including a glass coffee table and lamp in the living room and a computer in the den.

"What is it about this room that indicates a homicide took place there?" Kurtz asked.

"Nothing needs to be broken for someone to be murdered," Dismukes replied.

Another photo showed a TV cart in the Cooper children's bedroom that Adam said had been pulled away from the wall. Dismukes said he thought that the TV could have been in the room to occupy the children and that it could have been positioned to block the door.

"It's directly in front of the doorway," he said, to which Kurtz replied that the children, 2 and 4 at the time, were small enough to still get out of the room.

Dismukes also said the garage, previously described as being messy and unorganized, was clear enough that a car could have fit inside.

Outside the presence of the jury, defense attorneys asked Gessner to allow into evidence a statement from the Coopers' then-4-year-old daughter, Bella, who told a neighbor she saw her mother on the morning of July 12, 2008, wearing black shorts and a white T-shirt.

Dismukes said he never followed up on the statement because of the potential stress and trauma it could have caused a young child and also because Brad Cooper told police that Nancy Cooper left at 7 a.m. while Bella was still sleeping.

Gessner said, that at this point in the trial, he would not allow the statement, because it is hearsay, meaning the statement wasn't made directly to detectives.

On Wednesday, Dismukes testified that statements Brad Cooper had made and his reaction to news that his wife's body might have been found were also contributing factors in police considering him a suspect.

On the evening of July 14, 2008, investigators still had not made a positive identification of the body.

"Mr. Cooper was holding his head and groaning, but I did not see him cry," Dismukes said. "The groaning seemed a little strange and a little forced."

During a subsequent interview, Dismukes said, Brad Cooper commented that he believed investigators already thought he was a suspect. When police searched the couple's home, he questioned their authority to be there.

Prosecutors have said that, at the time of Nancy Cooper's death, the couple, both Canadian citizens, were in the process of separating and both had planned for Nancy Cooper to return to Canada with the couple's children.

In April 2008, however, Brad Cooper changed his mind, removed his wife's name from their bank and credit card accounts and took from her the children's passports to keep her from leaving, the state has said.

Defense attorneys have said the couple was struggling financially and that their client had to take such measures to keep them from financial ruin. He changed his mind about Canada, they said, because he realized he likely would not be able to see his daughters as often as he would have wanted.