“I Am Another You” is a movie that could almost have been conceived and designed to play at SXSW. It’s the second documentary directed by Nanfu Wang — though it was shot before her first, the guerrilla study of a Chinese dissident “Hooligan Sparrow” (2016) — and it’s a portrait of the kind of sun-dazed “rebel” street kid you perpetually see on the streets of a place like Austin, because he (or she) is drawn to its scruffy vibe of progressive tolerance.

In the opening voiceover, Wang recalls that when she lived in China, one of the only freedoms she had was her ability to travel; each year, she celebrated her birthday by going someplace she’d never been. After leaving her homeland in 2011 and transplanting herself to New York, she continued this birthday ritual by buying a one-way ticket to Florida, and it was there that she met Dylan Olsen, a 22-year-old homeless kid with wavy blond curls and photogenic tattoos who looks like the grunge version of a Renaissance saint. He’s skeevy and blissed-out at the same time, like the young Christian Slater as a vagabond surfer dude.

Wang decides that she wants to make a film about him, and the only way to do that is to adopt Dylan’s vagrant lifestyle, traveling around with him and recording his days like a diary. Since Dylan is young, sexy, and articulate and radiates a kind of becalmed togetherness, his desire to do nothing but move from place to place, sleeping in parks and eating out of dumpsters and boozing it up whenever he can, never seems less than a choice, and it raises a question that Wang sets out to answer: Why is he doing this? Is he just a miscreant, or is there something emblematic in his homeless-nomad mystique? We get bits and pieces of his past (he grew up outside Salt Lake City and despised the Mormon conservatism; he was a heroin addict from the age of 14 to 20), but mostly he exists in the present. “It’s the easiest life you could imagine,” says Dylan with his movie-star smile. “I’ll show you what freedom is like.”

We know in our gut that his explanation is too easy, but Dylan, for a while, comes off as part of a noble tradition of romantic American drifter-outsider. When he talks about being alive to the moment, or discovering people and things that he couldn’t have if he were rooted, he sounds like a dreamy wanderer high on Kerouac, or maybe a moonstruck tramp riding the rails in the ’30s. More than that, he’s got decades of middle-class hipster cachet behind him.

The hippies, of course, were the first to turn dropping out into something cool (in their eyes, it was essential to the awakening of the spirit), and by the 1980s, when the counterculture was just a fading memory, there were new waves of youthful dissolution to keep the tie-dyed dream alive. The Deadheads built up their own cult of communal aimlessness, and in Tompkins Square Park in New York, battles between the police and the homeless population acquired a dregs-of-the-’60s aura: Were they vagrants, or were they noble squatters who had the right to live wherever they wanted, man? Young people, it seems, have been running from the postwar middle class ever since it was invented, and Dylan Olsen bathes himself in the aura of a saintly glamour-boy misfit, an aura the movie itself gets caught up in. At times, he could be one of the kids in “American Honey” — glamorously pierced and bedraggled hip-hop roadsters who come on like they’re free, without acknowledging the ways that they’re lost.

Fortunately, “I Am Another You” does more than travel along with Dylan. The film unravels his mystery like a slacker detective story. Wang is a documentarian who works in a clear-eyed, guileless, strolling-around-with-a-camcorder way, yet she has a tough mindset that was forged by growing up in China, where — as “Hooligan Sparrow” made clear — not just the government but your neighbors can turn out to be your enemies. She wants to get caught up in Dylan and his road odyssey to nowhere, but a small revealing incident turns her off: He is given a bag of bagels by a sympathetic shopkeeper, and instead of bothering to tote it around with him, he tosses it away — because it interferes with his ability to beg more food. At that moment, she realizes he really is a wastrel, and that there’s something untrustworthy about him. So she cuts out.

That’s when the film starts to get really interesting. For a while, Wang presents another character: a veteran Utah police detective who works in the sex-crimes unit. He’s a solid dude we get to know and like, and then Wang reveals who he is: Dylan’s father. Was there some hidden abuse in the home? No. Dylan has a younger sister and brother, and we see images of him as a highly functional adolescent. Then, briefly, he returns home — for his father’s remarriage. There is bonding, and they seem like a family, touchingly so when Dylan and his dad and brother sing Crash Test Dummies’ “Mmm Mmm Mmm Mmm” (“There was a boy…whose parents made him come directly home right after school”). The mystery of Dylan starts to mingle with the hope that he’ll repair himself.

But then we learn what’s really happening, and it opens up the movie into a realm of haunted empathy. Dylan is mentally ill; we might have surmised that, but as naïve as it may sound, he doesn’t seem it. He hides it — the paranoid fear, the voices in his head that he’s convinced are the people he sees on the street talking to him. Watching “I Am Another You,” the responsible side of one — the therapeutic side — seizes on responsible answers, such as: “It’s a failure of the system. He needs to be on medication.” And, in fact, we learn that Dylan used to sell his medication for $300 a pop. (He also medicates himself with alcohol.) But, of course, that’s part of the illness. And by the end of “I Am Another You,” what starts off as a celebration of reckless freedom turns into a revelation of a broken yet soaring soul: the story of a life that resists being judged as much as it does being pigeonholed.