Sirius barely had time to register the amount of curses flooding his mind before he takes off after her. He'd agree that the situation was bad, for entirely different reasons. Namely that he did not want to have to deal with the police, go back to jail, or go into hiding again.

While he didn't have time to shift into his dog form, which did allow for a bit more speed, he was still plenty fast and managed to catch up. He doesn't want to do anything drastic (that won't help his case), but he's got to do something.

"Please, you've got to listen to me! I'm not a criminal!"