Yes, you need to file Form 1040X and amended state tax return and report the Form 1099R distributions on it.
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You will have to file Form 1040X. you will attach Form 1099R if federal tax has been withheld on it. The taxable portion will be subject to tax at your regular tax rates-depending on the tax bracket you are in. You may owe additional 10% penalty if this was an early distribution from the retirement plan.
If it is early distribution from the plan than you owe 10% additional penalty on your federal tax return.
Since federal income tax return is withheld you need to send in the form 1099 R with the tax return. Your total tax liability will be calculated and additionaly 10% (if applicable) will also be added. You will get credit for federal taxed withheld. Excess liability over the withheld amount is what you will owe to the IRS.