The short answer is that your state residency does not matter if you did not earn any income in New Mexico, Arizona or California. You do not have to file any state tax returns. Since you moved to California to stay in September 2020, you would file a California resident return next year.
We would need you to clarify your situation to determine your residency for 2020. I’m not sure what you mean by “lived in NM and went to school in AZ.” Going to school is considered a “temporary absence.” Students retain their permanent residency. If you lived with your parents in NM or had a permanent place there, you would be a NM resident until September and a CA resident for the rest of the year. AZ would not count.
Otherwise you would be a part-year resident in all three states, if you did not have a “permanent home” in New Mexico.
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