If you inherit cash that is not in an IRA or other retirement account, the inheritance is not taxable income and you do not report it on your tax return. Since it's not taxable income, there is no need to pay estimated tax. However, any income you earn by investing the inheritance after you receive it, such as interest or dividends, is taxable income. If the investment income will be substantial, you would have to take that into consideration in either adjusting your withholding or paying estimated tax.
If the person you expect to inherit from lived in New Jersey, the bequest might be subject to New Jersey inheritance tax. This is beyond the scope of what TurboTax handles. Normally the estate would pay the inheritance tax before any money is distributed to the beneficiaries. But if you are not the spouse or a direct descendent (child or grandchild) of the person you expect to inherit from, you should consult the executor or a local tax professional to determine whether you will have to pay NJ inheritance tax.
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