As a US citizen or green card holder, you are required to file a federal tax return and report all your world-wide income and pay US tax on it. You may qualify for the foreign earned income exclusion, but an IRA withdrawal is not earned income and will be taxed even if you have been living overseas for a long time. If you are also taxed on the same income in Japan, you may be able to claim a deduction or credit on your US tax return. There may also be tax treaty implications specific to Japan but I am not aware of any.
Your federal tax would be based on your total income, and be between 10% and 36%, plus the 10% penalty for early withdrawal. If you are not a bona fide state resident of CT (not domiciled in CT) then you don't owe CT income tax, even if withholding is required, and even if the address on the account is in CT. (However, if you don't pay tax in CT, they may send a letter asking for an explanation.)
If the trustee withholds CT state income tax, you can get that back by filing a state income tax return, reporting zero state income, in which case you don't owe tax and could claim a refund of the withholding.
You will be required to file the income on your tax return using the 1099-R that the plan will send. You may need to give them your current address, or make sure you can get the 1099-R online, or get it from your godmother if they mail it to her house. If the trustee doesn't withhold any tax, you will have to pay it, and if the trustee withholds federal tax, it might be more or less than what you actually owe, so you might owe more tax or be due a refund.
