But honestly, I think you’d be very lucky to catch any breaks if something went wrong while you took unusual initiative to go after a criminal. So do it at your own risk. I would probably take a small risk to catch a bad guy, but not too much. If you had an accident while chasing a bad guy, it wouldn’t shock me if you were prosecuted for reckless endangerment or the like. As with any other public policy issue, there are groups on both sides. Against you would be ranged the people who consider criminals victims of society (where society = you), and even some elements of law enforcement who would rather monopolize their physical role in limiting crime.
But hey, it’s fun to fantasize about becoming spider-man or superman, or otherwise play a good-vigilante role on behalf of the true victims of criminal thugs. I do it myself, and I only admire others who actually act on it.