James McNeil's wife watched on as he fell 25ft from the equipment at Bay Shore Camp on Thursday.
He was taken to hospital but was unable to be saved.
Police said they were looking into the possibility the harness malfunctioned.
Huron County Sheriff Kelly Hanson stressed that the camp's staff had full training and were certified and that Mr McNeil's death was being treated as an accident.
Bay Shore Camp is about 120 miles north of Detroit and welcomes church groups from across the States.
A statement on its Facebook page said: "We are deeply saddened by this turn of events.
"Out of respect for the family and friends of this individual, we have decided to postpone our Annual Benefit Auction to a later date.
"We ask that you hold all those touched by this tragic loss in your prayers."
A prayer service was held for Mr McNeil on Saturday.
