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You should report any income you received during the year on your federal and state returns. You should have received a 1099-R for your 401(k) distribution. There will be a 10% penalty for the early withdrawal and you will owe ordinary income tax on the amount withdrawn.
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Many states incorporate parts of the federal tax code and federal tax forms be reference. So, when you file your state return, it is assumed that you have already filed or will file a federal return. Some tax preparation software packages allow you to allocate income without filling out multiple copies of the same form, but if you are doing the return manually you may not have a choice.
The 401(k) distribution is only taxable in the state where you live. If you live in Virginia, then that is where you should report the amount shown on the 1099-R that you received.
An exception would be if the 1099-R shows withholding in another state besides the one where you live. You would need to file a return for that state as a non-resident to get the amount withheld refunded to you.
Generally speaking, your deduction should be allocated only to the state where you live, unless you have a deduction that was connected to another state in some way. For example, your home mortgage interest was paid in the state where your home is located.