Each state has different rules for what type of identification is suitable for being notarized. The California Notary Handbook does NOT specify if a Green Card, Resident Alien Card, or Permanent Resident Card may be used as identification for being notarized?
However, if you have a “California approved” (not sure what that means) identification card that has — a photograph, description of the person, signature of the person, and an identifying number: then you are in good shape.
Since a green card or resident alien card is not on the approved list of identification cards in the California Notary Public Handbook, it might be better to use a passport, state issued identification card, driver license, etc.
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Notarizing an ax-murderer in San Ysidro (he had to get his green card for the notarization)
Identification requirements for being notarized