You are going to have to check the taxing authorities for the states involved here (Secretary of State, FTB, Division Taxation, etc.) as state law varies.
A return will generally need to be filed in a state where the estate had state-source income (such as from a rental property located in a particular state) and generally where the decedent resided on the date of death.
There are states where a return is required to be filed if a trust or estate is being administered in that state.
