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No. In fact, unless the estate value exceeds $1 million, there is likely to be no tax effect at all.
There is likely to be no tax to you. The inheritance (state) and estate (federal) taxes are calculated by the estate and paid prior to the estate assets being distributed to the beneficiaries. The only time that a beneficiary is subject to tax at the individual level is when the assets inherited include the proceeds from an IRA or other pension account. This amount would be subject to income tax on the beneficiary's return in the year that it was received.