A power of attorney can be signed while in prison. Depending on where you are incarcerated, they may have forms there. If not, you may have to get in touch with an attorney in the area to draft one up for you and you can sign it in front of a notary. Regarding to changing your plea, in Washington, there are generally two types of pleas - a straight plea, and what is called an Alford plea, which states you don't believe you are guilty, but after reviewing the evidence against you, a trier of fact is likely to find you guilty, so in order to take advantage of a favorable offer by the prosecutor, you are nevertheless entering a plea of guilty to take advantage of the offer. Both show up as a guilty plea on your record. So I'm not sure why you want to change the form of your plea. If you were represented by an attorney when you entered the plea, it is unlikely the judge will grant you leave to change the form of your guilty plea as the sentence etc. would remain unchanged.
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You should let your attorney know both that you wish to sign over power of attorney and that you want to change your plea. It isnt unusual for defendants to want to execute powers of attorney prior to a long term incarceration; your attorney should be able to help you or know someone who can. And it is standard practice to enter a "not guilty" plea at arraignment - I 'm not sure in 22 years, I have ever had a client do otherwise. You can always change your plea at a later date. If may be that you wont be able to enter a "no contest" plea (what we call an "Alford" plea in WA) if you are charged in King County as the King County prosecutor's office is very hung up on defendant's "taking responsibility" when they enter guilty pleas. Speak with your attorney about the state's plea offer and whether the state will allow you to enter an Alford plea; sometimes when drugs/alcohol/mental illness prevent a defendant from recalling what s/he is alleged to have done, the state doesnt object to an Alford plea.