Prosecutor Joe Owmby said the state would leave the offer on the table until March 10 — 10 days before Yates' capital murder retrial is set to begin for the deaths of three of the five children in 2001.
Yates has pleaded innocent by reason of insanity, as she did at her first trial. The plea offer would require her to plead guilty or no contest to murder.
"We have rejected that recommendation," Yates' attorney George Parnham said.
Yates was convicted of capital murder in 2002, but the conviction was overturned because a forensic psychiatrist gave false testimony. Park Dietz had said an episode of television's "Law & Order" series about a woman with postpartum depression drowning her children was aired shortly before the Yates children died; the episode didn't exist.
On Monday, State District Judge Belinda Hill granted the state's request to hire a second expert witness to evaluate Yates. Parnham opposed another evaluation.
The judge also denied Parnham's claim that prosecutorial misconduct in the first trial would mean double jeopardy for Yates in the second trial. Hill found no evidence showing prosecutorial misconduct and no grounds for the double jeopardy claim.
During the first trial, psychiatrists testified that Yates suffered from schizophrenia and postpartum depression, but expert witnesses disagreed over the severity of her illness and whether it prevented her from knowing right from wrong.
A jury rejected Yates' original insanity defense and recommended life in prison for the drowning of three of her five children, ages 7, 5 and 6 months. Evidence was presented about the drowning of two others, ages 3 and 2, but Yates was not charged in their deaths.
By Pam Easton