In Golf tournaments there is generally not a dead heat for the actual winner of a tournament, as extra holes are played to decide the overall winner.
This is not the case for the 'placed' golfers. Most weeks will produce dead heats in golf events as lots of players finish with the same score.
When betting on the Top 3, Top 10, Top 20 finish, etc., the dead heat rule will be applied if there are players tied.
As an example, take a Top 10 finish bet on the PGA Championship in 2013. The tournament finished as follows:
Even though Scott Piercy and Adam Scott tied 5th, they would both be paid out at full odds on a Top 10 finish bet as they are within the top 10 players.
However, a top 10 finish bet on any of the players that tied 8th would mean that your return would be calculated as follows:
There are 3 places remaining (8th, 9th and 10th) but four players occupy these places. Therefore your return would be 3/4 your stake multiplied by the odds on your selected player.