RALEIGH, N.C. (AP) -- A North Carolina man was questioned about scratches and red marks on his neck the day his slain wife was reported missing but couldn't explain what caused them, according to search warrants unsealed Tuesday.

Bradley Cooper also told authorities he spent the day his wife disappeared scrubbing floors, cleaning the kitchen, washing laundry and other chores at their suburban Raleigh house.

Nancy Cooper was reported missing the afternoon of July 12 by a friend who told police the Coopers were in the middle of a divorce. Her body was found two days later, about three miles from their home in Cary, in a house-less cul-de-sac at the edge of a subdivision still under construction.

Bradley Cooper told police his wife went jogging that morning and never came home.

According to the warrants, police also questioned Cooper about why he had cleaned just the trunk of his vehicle and not the whole car. He said he had to clean up spilled gasoline, but no fuel smell was detected in the vehicle, the detectives said.

Hair was found in the car's trunk lid, on the front right bumper and the left front tire well, police say. The warrants did not say whether the hair has been identified as Nancy Cooper's.

No one, including Bradley Cooper, has been named a suspect in the homicide.

Authorities have said Cooper has cooperated and allowed them to search his home and vehicles. Calls by The Associated Press to Cooper and his attorney seeking comment on the warrants were not immediately returned.

The warrants also provided more detail about how Bradley and Nancy Cooper struggled to co-exist in the same house as their marriage crumbled after Bradley Cooper admitted to having an affair. After an attempt to reconcile, Nancy Cooper began working on a plan to get back to her childhood home in Canada and take their two children with her.

Bradley Cooper opposed the plan.

The couple each took a passport for one of the children so the other could not leave the country with both girls, the warrants stated. Nancy kept the one she had, along with her own passport and divorce documents, in the 2004 BMW X5 she drove.

The girls are now in the custody Nancy Cooper's relatives and Bradley Cooper is allowed supervised visits.

Bradley Cooper took his wife's name off all financial accounts and began providing her with an allowance to cover food and other daily needs. The day before Nancy Cooper disappeared, the couple had an argument about her making money by helping a friend paint at her home, the warrants say.

A friend of Nancy Cooper's, Jessica Adam, called police to the Cooper home the day of the disappearance. Shortly after they arrived, Bradley Cooper and the girls pulled up. He said when Nancy didn't come home by 12:30 p.m., they went looking for her.

Detectives spotted her cell phone and keys inside the home, the warrants say. The warrants say Nancy Cooper kept her keys and phone on her at all times so her husband wouldn't get them.

Detectives also noticed a dried stain on the white fitted sheet on the bed in the room where Nancy Cooper slept. Cleaning supplies were found in an adjacent bathroom.