According to Clearwater officials, two men were walking across the bridge shortly after midnight when they started talking about a dare for each of them to jump from the bridge. One man told officers that the other man jumped.
There was a delay of at least 30 to 45 minutes before it was reported. Detectives are trying to ascertain if the incident did occur.
Clearwater firefighters, along with the Coast Guard, are searching the area south of the Memorial Causeway bridge Thursday.
