Unlike most sequels, there's no reset button here. You pick up where Arkham Asylum left off.
Last week IGN previewed Batman: Arkham City and revealed that the Dark Knight begins the game with almost all of his gear he had when we walked out of Arkham Asylum. It's common in games, even sequels, to show you the full potential of a character and then strip them of their power and gear. This way, you know what you're working towards. That's not the case with Batman: Arkham City.
Developer Rocksteady confirmed that it won't "reset" Batman in Arkham City. The Dark Knight comes in to the criminally controlled section of Gotham fully prepared for the challenge ahead. In the 18 months since the events of Arkham Asylum, Batman has altered his gear in anticipation of the task at hand. He's not about to leave his wonderful toys in his other utility belt.
So rest easy, Bat-fans. You enter Arkham City fully capable of stomping faces. And you'll keep those tools as you explore the city.