While inherited cash is not taxed in the US, an annuity is not cash, it is a financial account. If it contains money that was not taxed previously (such as, if the owner bought it with pre-tax or tax-deductible funds, or if the owner bought it with after-tax funds but the gains have not been taxed) then the untaxed portion is taxed when the money is withdrawn, either by the original owner or by any heirs. You should receive a 1099-R from the custodian, enter this on your tax return.
