Massachusetts does not have an inheritance tax but it does have an estate tax. The estate, itself, will be responsible for paying any estate tax due and you, as executor, will be responsible for filing a federal and Massachusetts estate tax return, if necessary.
See https://www.mass.gov/guides/a-guide-to-estate-taxes
Regardless, as executor, you should absolutely consult with a legal and/or tax professional who is experienced in federal and MA estate and trust taxation (as well as probate procedure).
See https://www.avvo.com/
