Although it is never specified in the text, and although there is the possibility that Clarisse is alive with her family, who moved, it is accepted by Montag and others that Clarisse was run over by a car.
"Whole family moved out somewhere. But she's gone for good. I think she's dead."
"We couldn't be talking about the same girl."
"No. The same girl. McClellan. McClellan, run over by a car. Four days ago."
(Bradbury, Fahrenheit 451, Google Books)
Human life is of such little value in this society that no one but Montag seems to care that she has been killed; Clarisse mentions earlier that because people speed, and because people take great risks in order to feel, many of her friends from school have been run over. Later, as Montag is escaping, he is almost run down by a car full of kids, who are trying to run people down on purpose; he wonders if they are the same ones who killed Clarisse. The possibility of the government deliberately killing her to prevent her subversive ideas is unlikely; they were busy with the upcoming war.
We are never told exactly what has happened to Clarisse. Montag is starting to feel more things, and he is wondering what happened to the young girl. Clarisse was the one who made Montag remember a long forgotten memory from his childhood, so he wants to know where she is. In this society it is better not to ask too many questions. Mildred tells Montag what she heard and what she thinks happened to Clarisse.
No. The same girl. McClellan. McClellan, Run over by a car. Four days ago. I'm not sure. But I think she's dead. The family moved out anyway. I don't know. But I think she's dead.
Montag is starting to realize that everything is not okay. He is starting to feel things that the society wants people to forget. Montag is walking on dangerous ground now. Although we are never fully clear on what happened to Clarisse, we do know that she was a free thinker and to the society, that was a dangerous person.