The last First Four game is #11 Michigan's nothin' vs. #11 Tulsa's Captain Cane. Obviously, based on actual mascots that attend games, etc., Michigan would not even be in the bracket. They have a nickname, but no physical representation of that nickname like other schools do. They have done okay without one.
Michigan's non-existent mascot has a non-existent Twitter account.
They do have matching colors.