My Aunt in NC recently passed away and I'm one of the beneficiaries of the estate. I'm located in NH and about to receive a distribution, do I have to pay both state and federal tax on the proceeds from the sale of the house and distribution of some mutual funds/stock?

You owe no taxes at all on your inheritance, as there is no inheritance tax for the federal government, NH, or NC. If your Aunt's house was sold prior to distributing cash from the proceeds to the heir(s), then the estate may owe income tax on any gain realized between the fair market value on date of death and the actual proceds of the sale. But this is something that the executor of the estate has to take care of - you as an heir do not need to worry about payng any capital gains tax on the house. However, if the house was distributed to the heirs (retitled in your name(s) ) prior to its sale then you will have to report the sale on your income taxes. Again. Whether any taxes are due depends on whether you have a gain over your cost basis in the property, which is equal to the fair market value as of the date of your Aunt's death. Same thing with respect to sale of mutual fund shares - your gain or loss is equal to the selling prioce minus FMV on date of death.