No, you do not need to file a Rhode Island tax return simply for owning a property in the state. As you said, it does not produce income, therefore nothing would be reported on the return. If/when you sell the property in the future, a Rhode Island tax return would most likely be required.
As for your Federal return, you can enter the property tax paid for the Rhode Island property, but if you are not going to be using itemized deductions, then you do not need to enter it.
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