They're not related. You can start with either of them. There's something you will learn about by the end of the series' season 2 about the nature of the infection, you'll learn about the same thing at the beginning of the game's episode 2 (so if you play the game first, you'll learn about something you're not supposed to know about til the end of the series' season 2). I watched the series first because it came out long before the game. I suggest watching the series first. BTW, I enjoyed the game's story a LOT more, even though I'm a big fan of the series.
Will start watching the series tonight. I don't know how the series slipped under my radar until now. I remember all of my friend raving about it. --- PSN ID: Monti0 / XBOX LIVE Username: Monti 0 / Steam ID: Monti0