It is not taxed as an inheritance. It is taxed as a distribution from a retirement account. Distributions from retirement accounts (other than Roth accounts) are considered taxable income. It is included in your federal taxable income and in most circumstances your state taxable income. So yes, that is supposed to happen. Many states don't tax certain forms of retirement income, but you have to be over a certain age and inherited IRAs often aren't included in that.
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