TRAVERSE CITY — The hunt for the Griffin, a ship commanded by legendary French explorer La Salle, has taken an unlikely detour from northern Lake Michigan to a small-town hospital, where modern technology may help determine whether a wooden slab is wreckage from the 17th-Century vessel.

A team led by explorer Steve Libert, who has searched 30 years for the mysterious ship, hauled the roughly 400-pound beam ashore in June. He discovered a 10.5-foot section of it protruding from the lake bed in 2001 during a dive near uninhabited Poverty Island, and received permits this summer to dig beneath it. But his crew discovered the beam wasn’t attached to anything.

Disappointed but undaunted, Libert said his next goal is determining the age of the tree that produced the timber and when it was cut down. He said the beam could be the bowsprit — a spur or pole that extends from a vessel’s stem — of the Griffin, which disappeared with its six-member crew and a cargo of furs in 1679....