Since "Sleepy Hollow" opens with a societal complication, it can be classified as a tragedy. The problem is developed through the “tragic flaw” of the hero and it signifies greed or ego. The problem is key to our human identities, and not just portrayed by an outside force. The fault uncovers the truth about the problem. The tragedy ends with the solution to the problem -- justice, often accompanied by the death of the tragic hero.

I would say it is neither. A comedy needs to have a happy ending in which social order is restored. A tragedy doesn't just mean that bad things happen, but that a person of some stature has her or (usually) his life shattered due to the very nature of his character. Neither of these fully apply here.

I would call this a romance, in the older meaning of the term.