No, only choose your 'home' State (the State where you reside and call home) as your State for tax purposes. You will only pay State income tax to the State where you live, not the State where you earned or qualified for the pension.
Effective for retirement income received after December 31, 1995, federal law prohibits any state from taxing certain retirement income (mainly pension income) unless you are resident of, or domiciled in, that state. For example, if you receive a pension from your former California employer and you now reside in New Mexico, California may not tax your retirement income. Because you are now a New Mexico resident, your retirement income is taxable in New Mexico.
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