When Montag thinks that Mildred overdosed on pills, he realizes he would not cry if she were to die because he feels no connection to her.
Montag has begun to realize that his entire society is empty. His people are lost. He does not even feel a connection with his own wife. He responds in anger, not sadness, when he thinks she might take too many pills.
For it would be the dying of an unknown, a street face, a newspaper image, and it was suddenly so very wrong that he had begun to cry, not at death but at the thought of not crying at death, a silly empty man near a silly empty woman… (Part I)
Montag knows that suicide is common in his world. He remembers seeing the technicians with their “electronic-eyed snake” as they pump the stomach of the woman who tried to commit suicide. It is a regular occurrence. Picturing this happen to Mildred does not make him sad—it makes him angry.
Montag longs for a deeper connection, and knows he can't have one with his wife. This is why Clarisse makes such an impact on him, and why he is drawn to the books.