How do I file state taxes for California and New York after marriage

Hi, I have faced a challenge in terms of state tax filing and hope you can help me.

My wife and I got married last year. She has lived and worked in New York until October, she then quit job and moved to California. I have been living and working in California for the whole year. In this situation, how should we file taxes?

For New York, must we file separately? My wife has to file resident, and I have to file non-resident? Or can we file MFJ? We would prefer MFJ.

For California, given my wife has no income in California, can we just file MFJ as resident?

However, in TurboTax software, when we started state tax, it prompted us to file nonresident for New York and resident for California. Do I need to change them?

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