No one likes to be called by the boss to his/ her office and sit through a long discussion. But in any case, leave with peace and show respect to your dept head (regardless of you liking this person or not).

Back then I did not know the procedure and I handed the letter to HR. Our HR asked me to pass the letter to the boss instead and I did just that.

So I guess in the end it's better to pass the letter to the boss first, listen to what he/ she has to say then pass another copy to the HR.