The personal representative of an estate will have to file a final income tax return for the part of the year in which the decedent was alive. This applies to both federal and state income tax.
For income tax purposes, the state and federal government look at an estate as a separate person who has to pay tax on income received. To the extent that the estate receives income in the form of dividends and capital gains, it will have to file a fiduciary income tax return for each year in which it is open. The same rules apply to a trust. The trustees are required to file fiduciary income tax returns on income received by the trust.