CBS (NYSE: CBS) Mobile has launched a free Harper’s Island application on the Apple (NSDQ: AAPL) App Store to promote its new show—Harper’s Island. The show is a murder mystery where not even the cast know what is going to happen the following week, and the app is designed to get people to interact with the show. The pre-launch version of the application provides iPhone and iPod touch users with details on the terrifying history of Harper’s Island, as well as preview clips from the show.

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The show premieres in two weeks, at which point the app will get updated so viewers can participate in the mystery by watching preview and summary clips from the television broadcast, navigate the interactive island map, learn more about the island’s guests and review the local newspaper, Harper’s Globe, for even more details. They then try to guess the next victim, and the murderer. People get points for accurate guesses and are listed on a leaderboard. This is a natural evolution from the text-based interaction that TV shows have used in the past, and the iPhone is a good place to test it. CBS already has an iPhone version of its TV.com site.