The National Transportation and Safety Board says the mate "exercised his Fifth Amendment right and refused to meet with investigators" over the weekend.
U.S. Coast Guard Capt. Todd Gatlin tells The Associated Press the mate was on duty as the tug pushed a 250-foot barge up the Delaware River.
The NTSB says the duck boat's crew said radio calls to the tug "received no response."
The agency says the tug's crew consisted of a captain, the mate, an engineer and two deckhands.
The collision last week sunk the tourist vessel, dumping 37 people overboard and killing two young Hungarians.