Technically, The play Romeo and Juliet is neither a tragedy nor a comedy.
The play does not fit the classical definition of tragedy. In a traditional tragedy, there must be a main character who begins as a good person, but has a fatal flaw that leads to downfall, and eventually, death. Before death, that main character must also have a moment of insight, and express some form of awareness that there has been a fall from grace.
None of the characters in Romeo and Juliet fulfill all of these characteristics. Friar Laurence comes closest. However, even though Friar Laurence does evidence a fatal flaw, downfall, and insight, he does not die.
Romeo and Juliet both die, of course, but they do not show evidence of the progression required to be considered tragic heroes.
So, Romeo and Juliet is not easily classified as a tragedy.
A Shakespearean comedy has a lighthearted tone and typically ends with the marriage of several characters, or another celebration of some sort. I think we can all agree that Romeo and Juliet does not fit with this definition of comedy.
Therefore, Romeo and Juliet is not classified as a tragedy and does not fit the requirements of a comedy, either.