STEPHENVILLE, Texas (AP) -

The death-penalty case against a North Texas man accused of killing former Navy SEAL sniper Chris Kyle and another man remains on track for a May trial.

State District Judge Jason Cashon heard more than 40 motions Tuesday in the case of Eddie Ray Routh, charged with capital murder for the deaths of Kyle and Chad Littlefield at a shooting range.

Cashon refused to set aside the indictment against Routh, whose attorneys argued Texas' death penalty statute is unconstitutional.

The 26-year-old Routh appeared in court in a jail uniform and ankle chains.

He is to go on trial May 5 in Stephenville, about 100 miles southwest of Dallas.

Kyle is reputedly the deadliest sniper in American history, and later wrote a best-selling book about his life at and after war.