Doesn't hurt to get multiple opinions in here I guess.
Sometimes you might be having a really bad streak of people that just like to run. I have had this happen countless times. This happens A LOT when you are ordering someone out of the car with E. I would say they will run 95% of the time. Its a game mechanic. Not sure if it will be fixed in LSPDFR 0.3 or not. For some reason the person in the car doesn't look at you as a cop but a crazy person with a gun.
Also do like mentioned above. You can try and taze them, sometimes they might comply and other times they will not. Also there seems to be a weird bug that happens sometimes, that allows you to still play LSPDFR, you can even do a pull over, yet the moment you point your gun they run and you can't arrest them. BUT if another AI cop arrives all of a sudden the person complies? Yes very strange.
Here is how I fixed those situations. Bring down your Rage Console (Default to F4). Go ahead and type in LoadPlugin LSPD (Now just press Tab) it will finish the sentence for you. You will be left with this on your screen in Rage Console LoadPlugin "LSPD First Response.dll" Just press Enter. wait about 10 seconds, it will reload. NOW JUMP and PRESS F9 at the same time. (Note your cop model will change appearance) now try and arrest someone, should work. But once again don't point the gun at them in the car as they will just flee. Instead, ask them out of the car and then point your gun. The new arrest mechanics in LSPDFR 0.3 will probably resolve all of this issue and I can't wait as you do not even need to point a gun anymore if you do not want to.