You just inherited money from a relative who died in New York you live in Rhode Island which has an inheritance tax transfer tax Are you responsible for the RI tax?

First, Rhode Island doesn't have an inheritance tax, it has an estate tax - there is a difference but unless you are going to be handling interstate estate matters, don't worry about it.

Regardless of whether Rhode Island has inheritance tax or an estate tax, if the deceased was a New York resident and the property was in New York, only the New York taxes would be levied.

New York would collect the taxes from the estate, however, if the executor somehow paid you and didn't pay the New York taxes then New York could collect the taxes, penalties and interest from you.

Tax attorney/CPA