I love how people in this thread are somehow able to make an accurate assessment of all details based on a two second segment (being generous here) of the girl running and the cop pulling the taser behind her. Whether she was in grabbing distance or not is not for you to decide. Sure, it is possible that the policeman could have caught her if not the taser, but maybe not - what if she suddenly sped up? These two weren't on a racing track but in a building, which, you should remember, have corridors and turns. Also, you should remember that when running, you tend to slow down in order to make a turn. It's perfectly plausible that the girl would have gotten away, if the cop tried to just sprint after her.
Also, he clearly didn't mean to harm her (well more than tasing, that is), when reading some comments I might assume that the guys was either a precog or clearly thought "Now, I'll paralyse her and she'll fall down, hopefully hitting her head. If I'm lucky, I might kill her." He might have not realised that would happen but he did not intend it to happen.
I'm not defending the guy, whether tasing was needed or not I cannot say but saying "he could have totally caught her" or implying that he meant to put her in hospital is just wrong.