Signing the lease doesn't mean you moved yet.
The state you were a resident of on 31 Dec is the controlling factor, so you had to physically move between states before 1 Jan 2021.
Now if you moved to a temporary residence/apartment in the new state earlier in 2020, then you can use that date as your "move" date. Otherwise, you were a resident of the former state for the whole year of 2020.
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Now, it certainly is possible to move into a new residence on 1 Jan 2021...in that case, you don't indicate a move for 2020 either...and are considered a full-year resident of the former state....with no "move" involved. Then when you file 2021 taxes in early 2022, you are a full-yr resident of the new state with no "move" involved. Of course, either state may have questions later about why you never filed a part-year tax return, so you'd better keep receipts/charges....all receipts possibly needed to show you moved on 1 January....and had charges in the new state on 1 Jan and the days after. I have no idea what proof they would really want.....just a guess.
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Your current mailing address is immaterial, and does not control anything for indicating a move.....the mailing address is just where you are now.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
