Effectively yes, you can do that as a cop in most justice systems if you can dress up the "seems shifty" in a bit more concrete terms.

But if there is nothing to back it up, the guy will be realeased very soon, and if you do it repeatedly, you'll eventually get problems (and rather quickly and seriously if you lied and it can be proven).

A little bizarre to see "them" followed by "he"...

I guess the question here is what about him makes him seem shifty to you. One would at least hope his skin color would not be factoring into that and that your judgment would have been the same for anybody else exhibiting the same behavior.