Do I have to have wifi or Internet connection to watch a rented movie

No, but you need a Internet connection to download the movie.

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From my own personal experience, I have found that when I turn off the Wi-Fi on my Wi-Fi only iPad, I am still able to play rented movies on it. I have tried this perhaps four or five times and in each case, this has been the result. I have also noted that other users have had the same experience as I.

However saying that I have noted a small number of users that have stated they are unable to view rented movies without an Internet connection. This knowledge base article from Apple, also suggests that an Internet connection is required.