No, there's no penalty in any of the street crimes for killing a suspect rather than capturing them alive, if the option is given to you.
If you kill someone who you must capture alive, you will fail the street crime.
Usually the game will make this distinction clear to you when you start the pursuit.
I should mention that if you're interested in achievements (and your platform supports them) there are achievements for tackling a suspect and for firing a warning shot to stop a suspect, which you sometimes have the opportunity to do during street crimes. These only count after the tutorial missions (ie, once you become a full fledged detective) However, you can always replay a case or street crime later, so these are not missable.