Death penalty foes are concerned that Kentucky's method for lethal injections doesn't include a plan if the execution goes bad.
They say a lack of a plan could lead to a long, painful death that could be considered unconstitutional.
A spokeswoman for the Department of Corrections says the Supreme Court upheld the state's lethal injection methods in 2005.
Death penalty opponents note that in Kentucky's last execution, in 1999, officials needed two tries to find a vein in Eddie Lee Harper's arms.
Convicted cop-killer Ralph Baze is scheduled to be executed later this month.