Update: Tennessee used to impose its own estate tax, which it called an "inheritance tax." This tax ended on December 31, 2015. For deaths occurring in 2016 or later, you do not need to worry about Tennessee inheritance tax at all. The following is a description of how the tax worked for deaths that occurred prior to 2016.
What Tennessee called an "inheritance tax" was really a state estate tax—that is, a tax imposed only when the total value of an estate exceeds a certain value. Under Tennessee law, the tax kicked in if your estate (all the property you own at your death) had a total value of more than $5 million.
The taxes that other states call inheritance taxes are not based on the total value of the estate. They are imposed on the people who inherit from you, and the tax rate depends on your family relationship. Close relatives are either exempt from tax or pay a low rate, while more distant relatives or unrelated persons are taxed at a higher rate.
State estate tax is also separate from the federal estate tax.
It's the job of your executor to determine whether or not an estate tax return must be filed with the state. For deaths in 2015, if the gross estate of a Tennessee resident has a value of more than $5 million, the executor must file a state inheritance tax return. No estate tax return must be filed for any deaths after 2015.
Even if a return must be filed, it doesn't mean the estate will owe tax. Deductions are taken from the gross estate (which is pretty much everything you own at death, as discussed below) to arrive at the taxable estate. If the taxable estate is lower than the estate tax exemption, no tax will be due.
Common deductions include expenses such as funeral costs and attorneys' fees. Also, assets left to a spouse are not taxed, regardless of amount.
The estates of some nonresidents also have to file a Tennessee inheritance tax return. If a nonresident owned valuable assets physically in the state (real estate, for example), the estate may need to file a state inheritance tax return.
Your gross estate, for tax purposes, includes what you own as of your death:
Some property that you don't actually own at death may also be counted in your estate, for estate tax purposes. If you made taxable gifts (more than the annual federal gift tax exclusion amount, which is currently $15,000 per year per recipient), within three years of your death, then those gifts must be included in your gross estate. The amount of gift tax you paid, however, can be taken as a credit.
If an estate tax return is required, the executor must file it within nine months of the date of death (or apply for an extension). Any tax due must still be paid by the original deadline, or interest begins to accrue on the unpaid amount.
The Tennessee Department of Revenue website provides forms and information about the tax. But an executor will need to hire an experienced local lawyer or CPA to prepare the return. The fee can be paid from funds in the estate.