Conduct of this sort has been reported in many jurisdictions as lacking professionalism and ethics. The fact that a prosecutor did this while in the ear shock of jurors is a manifestation of the fear he or she is experiencing in this case. Apparently, that Deputy DA may have doubts about the case. It's possible they may be intentionally trying to get a mistrial or illegally persuade the jurors. It is improper conduct and the judge may declare a mistrial if requested by the defense. It may require a hearing with the jurors by questioning each whether or not they heard such statements and if it effects their decisions in the case, however.
It was not professional, but probably not a basis to get fired. I am assuming given that the court was recessed, that no jury, witness, or judge heard the exchange. If such a comment was made in earshot of the jury, it would be a basis for a mistrial.
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Can she? Anyone can do anything. Should she have? Absolutely not. Her conduct was unprofessional and should be reported to her supervisor.
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It could be worse. One day while waiting for my case to be called, a sentencing concluded, and off the record but quite loudly the DA leaned over to the two defendants and said "This is the last break you get in my f*cking court you little bastards. Come back here again, motherf*ckers and I am going to f*ck good." Neither the judge nor the defense attorney reacted.
The defense attorney should make a record of this in the court. Move for a dismissal. I would suggest briefing the issue. In the alternative a mistrial. Lastly this DA should not only be reported to their supervisor but a formal complaint with the State Bar should be made.
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Her behavior and comments are unprofessional. However, they also reveal the strength of the defense. Most DA's seek verdicts in easy cases to impress their supervisors. Her outburst is an attempt to avoid a trial she fears losing. Pick 12 good jurors and beat her in trial!