Is it a comedy
That's about it
And I really really hoped I wouldn't die
It's more of a mystery with comedic moments.
_______
The sun is shining... but the ice is slippery.
There is a passage where Josh Hartnett tries to pull if accents. I'm pretty sure that was comedy...
But you can have moments of humour or light hearted characters in films of any genre without the film being classified as a "comedy".
Hartnett and Liu's characters are playfully goodhumoured with each other, but overall the story arc for Hartnett's character is violent tragedy and revenge (or righteous vengence, depending on your point of view).
Liu's character and Slevin's relationship with her is essential to soften and humanise Slevin's character so viewers relate to him as a person, otherwise it's just a story of deliberately planned, cold blodded revenge killings... which is not commonly classified as comedy.
As I watched this movie I was thinking of it as a tongue in cheek crime drama. Kind of a lighthearted movie where you don't take the killing too serious, like in True Lies. I had looked at the IMDB page before watching and saw it classified as "Crime, Drama, Mystery" and was wondering why they didn't throw in "Comedy".
But the movie became progressively more serious as it went along until I finally realized: "NO, not a comedy."