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Let me clarify something about taxes: you only owe for the one year in the old state. Let's say you moved now (April 17) and started working in NV. You would only owe in CA for Jan - April (2017) *IF* you even owe taxes. If you're getting a refund, you can still file for that in NV. There are lots of places that do taxes for you for a small fee. You're not expected to know all of those laws.
So, be sure to tell your former employer where to send your W-2 for 2017 when you move.
As for "bureaus" needing to "find" you, if you have a green card, you have to let them know your new address, as mentioned. American citizens don't have to do that.