At this point in the story, the significance of May's immediate outburst into song is somewhat unknown, but certainly brings up alarm and the question of what this might be foreshadowing.
What is known in this scene is that May is giving a brief explanation of the "Calendar names" of the sisters. She mentions, "We had an April, too, but..." From this quote it can be assumed that April is now dead.
What will later be revealed is that April was May's twin sister, who committed suicide. May is a particularly sensitive character, who sings whenever she is faced with something particularly emotional or difficult. In chapter 5, Lily gives credit to Rosaleen for figuring this out:
She said if you kept things on a happy note, May did fine, but bring up an unpleasant subject...It seemed to be her personal way of warding off crying.