While lawsuits against the police were and are very prevalent, the circumstances shown here would greatly diminish the likelihood of a favorable verdict for the plaintiff- or of an attorney taking the case. He fled from the police, and he ran into traffic- both of which are violations of California law.
When the (wrong) suspect is explaining himself to Hunter in the interrogation room, he asks Hunter if he wouldn't have also ran in those circumstances. Hunter replies that he doesn't know as he's never killed anybody. It's likely that he meant he's never murdered anybody, as throughout the seven seasons of the show in almost every episode Hunter shoots someone dead and has thus killed plenty of people.
It's unethical for a lawyer to solicit a client as done here. It could be grounds for disbarment. Beyond that, the events surrounding the arrest would not have enough likelihood of success for an experienced lawyer to pursue it, especially since the suspect freely chose to run before he was accused or restrained. The part about knowing docs who will maximize degree of injury for plaintiffs or minimize them for defendants is real.