In Washington a codicil needs to be witnessed the same way that a will does. Washington Statute prescribes that the testator's signature on his or her will be witnessed by two witnesses. While the statute does not require that the testator's signature be notarized, it is good practice to have your will notarized in addition to obtaining the signatures of two competent and disinterested (not inheriting under the will nor related to the Testator) witnesses.
Agree with other answers. Not required but a good idea. The codicil NEEDS two witnesses. However, without a notary -- who is actually notarizing the witness signatures -- the court requires a verification process that includes trying to track down the witnesses (or at least showing an attempt to do so) after the testator has passed away. Good luck with that! So it is far easier to just go through the extra step of having a notary sign the will as well.