Do I need to buy a higher class SDHC card for the Kodak Zi8 pocket video for 1080p HD?

I'm thinking about purchasing the Kodak Zi8. It comes with an expandable SD/SDHC card slot up to 32 GB. Will this card be enough to shoot in 1080p HD? Or do I need to buy a separate SDHC card that's a class 6 or higher? I saw a review that stated I needed to buy a faster one for HD but I think that review was a bit outdated. I couldn't find out what class the card was that came with it. It makes sense that the card that's given with it is good for HD 1080p but I wasn't 100% sure and need re-assurance. Thank you.