Hawaii residents are subject to an estate tax if they leave an estate of more than $5,450,000. This tax falls on the estate of the person who died; the beneficiaries or heirs inherit what's left. There is no inheritance tax in Hawaii; this would be tax that falls on the heirs and beneficiaries, not on the estate of the person who died.
This state estate tax is in addition to the federal estate tax, which also falls on the estate of the person who died, not on the people who inherit that property. There is a federal estate tax exemption of $5 million, which is indexed to inflation and is currently $5,450,000, and only people who die with an estate larger than that exemption will have to pay estate tax. It is estimated that only the richest .14% of Americans will be subject to the estate tax at all, or only two out of every 1,000 people who die.
If someone dies in Hawaii with less than the exemption amount (currently $5,450,000), their estate doesn't owe any federal estate tax, and if someone dies in Hawaii with an estate worth less than this same amount, there is no Hawaii estate tax, either. The heirs and beneficiaries inherit the property free of tax. They don't pay income tax on it, either, because inherited property is not ordinary income. The only exception to this are inherited retirement accounts, which are subject to income tax as the assets are withdrawn.
Hawaii, like the federal government, allows a surviving spouse to use the unused portion of a deceased spouse's estate tax exemption. This rule is called portability. For example, if the first spouse to die uses only $1 million of his estate tax exemption, his surviving spouse could use the rest. To take advantage of this provision, however, state and federal estate tax returns must be filed at the death of the first spouse to die.
For background information and tax forms, see the Hawaii Department of Taxation website.