R.I. Gen. Laws § 39-6-33
If the railroad shall agree with the acquiring authority upon the sum to be paid, and the price shall be approved by the state properties committee, the sum agreed shall be paid to the railroad upon delivery of proper instruments of conveyance. If no agreement as to the price to be paid is reached within one year following the abandonment, then within six (6) months thereafter, or if the abandoned right of way has not been disposed of otherwise, then at any time thereafter, the acquiring authority may petition the superior court for one of the counties in which the land is situated for an assessment by a judge thereof of the fair value to be paid for the estate or interest in the land. A hearing on the petition shall be conducted as in other civil actions, and either party shall have the right to appeal the decision as provided by law. Within thirty (30) days after a final judgment is entered, the acquiring authority shall tender payment in accordance therewith to the railroad and receive proper instruments of conveyance. If the acquiring authority shall fail to make tender within the time allowed, the railroad shall be at liberty to dispose of the land or any estate or interest therein in any manner it shall see fit.
R.I. Gen. Laws § 39-6-33