Over several days of witnesses' testimony, prosecutors reconstructed the day two years ago when they say Routh, 27, killed Kyle and Kyle's friend Chad Littlefield at a gun range about 70 miles (110 km) southwest of Fort Worth, stole Kyle's pickup truck and was taken into custody following a high-speed car chase.
Routh's lawyers have not contested accusations that Routh fired the fatal shots. They have contended he was psychotic and did not realize what he was doing.
They are trying to have him declared innocent by reason of insanity and said in opening arguments they would call expert witnesses who will attest to Routh's troubled mental state.
Prosecutors are seeking life in prison without the possibility of parole in the trial held in the rural town of Stephenville before a jury of 10 women and two men.
The prosecution has shown police videos of Routh leading them on a chase and confessing to the murders in a rambling speech. Before being taken into custody, police said he told them he "had taken a couple of souls."
Just before resting their case, prosecutors presented a recorded phone call Routh had in jail with a reporter from the New Yorker magazine, where Routh again confessed to the killings and said: "I took care of business and left," Dallas broadcaster WFAA reported.
Routh, who was with the U.S. Marines in Iraq and Haiti, was driven to the range by Kyle, who had been helping fellow veterans heal the mental scars associated with fighting. Prosecutors said Routh did not take part in combat.
As the three men sped over Texas country roads, Kyle, who was credited with the most kills of any U.S. sniper, sent a text to Littlefield that read: "This dude is straight up nuts," defense attorney Tim Moore told jurors.
