Reader Tina points to this video, which purports to show young women walking down the street touching strangers' hair, video-recording the process throughout. For a likely higher degree of annoyance to others, and a certainly much higher degree of danger to the petters, see two young men doing the same.
(1) Real or fake? I'll assume real for purposes of the question. I'll also assume that it's in New York, as accounts suggest.
(2) Is it a crime, asks the reader? Oddly enough, I don't think so. It's not assault or attempted assault under New York law, because it involves no actual or attempted physical injury. It's not a sex crime, because it doesn't involve the touching of "sexual or other intimate parts" (hair can be intimate in some senses, but not, I think, in the sense contemplated in that phrase). It's not menacing, because it's not likely to create a fear of "physical injury" (or at least not enough such fear, I'd guess). It's not criminal harassment, because it doesn't involve placing some in reasonable fear of physical injury, repeatedly following the person, or action done with the intent to harass, annoy, or alarm.
Some states seem to have laws banning "offensive touching" (see, e.g., 11 Delaware Code § 601(a)(1), barring "[i]ntentionally touch[ing] another person either with a member of his or her body or with any instrument, knowing that the person is thereby likely to cause offense or alarm to such other person") or "offensive physical contact" (see, e.g., Alaska Statute § 11.61.120). Under these laws, we'd have to figure out whether having one's hair touched for fun (as opposed to having one's hair touched by someone who's trying to brush off a fly, or by someone who's simply trying to make room for himself on a crowded subway) is "offensive" enough; I suspect it would be, but I'd have to do more research to figure this out.
There may well be other statutes that my quick research hasn't found -- please do let me know if you can find some. But for now I can't see a New York law that makes this hair petting illegal.
(3) Is this the tort of "battery"? Yes, if it's "offensive bodily contact," which is to say contact "that a reasonable person would find offensive," because it "offends a reasonable sense of personal dignity." (See above.)
(4) Could this also involve the tortious use of another's likeness for commercial purposes? (The Petting Game people seem to have some commercial motivations, though I'm a little hazy on their business model.) I doubt it, for complex reasons, especially under the New York law of right of publicity, which is relatively narrow.
(5) Do I recommend such behavior to thrill-seeking New Yorkers? No, I don't.