First, I would say there is an overriding passive/disconnected tone to the book. This is evidenced first by the 3rd person point of view. The action is often seen from a distance - which emphasizes a disconnection - certainly there is evidence of disconnection between characters, disconnection from reality, disconnection from desire, knowledge, truth, etc.
There is also an ironic, paradoxical tone in this novel. Consider, for example, the use of the mechanical hound to sniff out books. Arguably, this is a pretty important job in the society presented, and it is carried out by a robot. Paradoxically, characters like Mildred, do not really have any important responsibilities, and actually appear more robotic than the robots. This is intentionally ironic - used to heighten the sense that when/if the world stops caring - people will become more like robots and we will have to create robots to get things done.
Finally, I would not go so far as to say there is a morbid tone, but certainly the tone throughout the novel is very somber. This means, basically, serious. Although it is a work of science fiction - the ideas of censorship, loss of knowledge, loss of the persuit of knowledge - these are very serious ideas that if played out in reality at even a fraction of how they play out in the book - could result in very serious consequences. I'm sure you noticed this is not by any means, a lighthearted book. Even the humor is dark. Bradbury's intention here was clearly less focused on entertainment, and more focused on the deeper message.