1. At any time before the commencement of the trial of a homicide offense, the defendant may, with the assent of the court, waive a trial by jury and agree to submit all issues in the case to the court, whose finding shall have the force and effect of a verdict of a jury. Such a waiver must include a waiver of a trial by jury of all issues and offenses charged in the case, including the punishment to be assessed and imposed if the defendant is found guilty.
2. No defendant who pleads guilty to a homicide offense or who is found guilty of a homicide offense after trial to the court without a jury shall be permitted a trial by jury on the issue of the punishment to be imposed, except by agreement of the state.
3. If a defendant is found guilty of murder in the first degree after a jury trial in which the state has not waived the death penalty, the defendant may not waive a jury trial of the issue of the punishment to be imposed, except by agreement with the state and the court.
4. Any waiver of a jury trial and agreement permitted by this section shall be entered in the court record.