She turned the world on with her smile. But where will Mary Tyler Moore’s hat land?

Hollywood is filled with small-time crooks: stars who boast on red carpets and late-night talk shows about swiping mementos from set. Bryan Cranston made off with Walter White’s porkpie hat from “Breaking Bad”; Ariana Grande lifted a pair of prosthetic ears from “Wicked.”

One might assume that Mary Tyler Moore would have wanted the Hat from the opening titles of her 1970s hit series, “The Mary Tyler Moore Show.”

In what may be the most famous freeze frame in television history, Moore’s character, a Midwestern sunburst named Mary Richards, removes her tufted tam-o’-shanter and, right in the thick of bustling Minneapolis foot traffic, tosses it skyward — as purely ebullient an image as Hollywood has ever produced. The moment has been aped by “Scrubs” and “The Simpsons,” and immortalized in bronze at the site of the throw. In an opening title sequence that was forever being tweaked throughout the show’s seven seasons, The Hat was a constant.

So: How did she manage to keep it?

“Well, you have to remember: She owned the company,” her husband, S. Robert Levine, gently explained. “I think someone put it in an envelope for her.”

Fair enough. As the eponymous MTM of MTM Enterprises (the production company behind all 168 episodes of the show’s 1970-77 run), Moore did not exactly need to break into the costume department after dark to claim her piece of history. But neither did she treat the woolen cap like a conversation piece or hunting trophy: She did not, for instance, bring it out at parties.

“It wasn’t something that we were passing around, no,” Levine said with a laugh. Moore had kept The Hat hidden away in a file drawer in her office for years. “It was only when I started to dig into everything that I found it.”

This spring, he sold the sprawling Greenwich, Connecticut, estate where the couple spent the last of their 33 years together for $16.9 million. And in June, a Doyle auction brought together 347 lots from the actress’ estate — including the golden capital M that hung on the wall in Mary’s apartment in “The Mary Tyler Moore Show.” (Lena Waithe, who produced the HBO documentary, bought it for $35,200.)

“It’s a big loss — I have to acknowledge that,” said Levine, 71. “It’s a loss stepping away from that beautiful home that we created together and all the things that were in it. But it was the right time.”

The auction included bracelets (Tiffany, Cartier), portraits (Annie Leibovitz, Al Hirschfeld) and several knights-in-shining-armor’s worth of sterling silver. Not up for bidding: Moore’s woolen tam-o’-shanter or, for that matter, any items from her personal wardrobe.

It was not an oversight. By the time the auction came together, Levine already had other plans for his wife’s considerable collection of Armanis, Scaasis and Issey Miyakes.

One year after his wife’s death, Levine, a retired cardiologist, took the first step toward creating the Mary Tyler Moore Vision Initiative, a nonprofit dedicated to ending diabetes-related vision loss and blindness. Moore was a Type 1 diabetic, and she struggled with diminishing vision for years. By the end of her life, he said, she was nearly blind.

The search led to Elyce Arons, co-founder of Kate Spade (the brand), best friend of Kate Spade (the woman) and a Mary Tyler Moore fan since girlhood. At the time, Arons was preparing for the publication of a memoir recounting her more than three decades of friendship with Spade. Its title, “We Might Just Make It After All,” is a riff on the chorus of the “Mary Tyler Moore Show” theme song.

Arons met her future business partner, then Katy Brosnahan, in August 1981 on her first day at the University of Kansas. Both young women were pursuing majors in journalism, and both, Arons soon discovered, because of a fictional local TV news producer named Mary Richards.

“Mary was a modern woman,” Arons, 62, said recently in the New York showroom of Frances Valentine, the second fashion brand she started with Spade. “She was single, she was confident, she made women of my generation believe that we could do that.”

Now Arons is in business with Mary Tyler Moore, in a way.

To raise money for the foundation, Arons and the Frances Valentine team set about creating a capsule collection for fall 2026 with designs inspired by two of Moore’s earliest characters, Laura Petrie on “The Dick Van Dyke Show” and, of course, Mary Richards.

In March, Levine came down to the city from Connecticut to get a feel for the brand. Evidently he was pleased with what he saw: He invited Arons to Greenwich to browse his wife’s closet. She did not need to be asked twice.

“I was like, ‘When?’” she said.

The day of the visit, Arons gushed just about as much as one might expect from someone given free rein in her hero’s wardrobe. Video of the day shows Arons stepping out and giving a twirl in one look after another, makeover-montage style. “It was like Christmas morning,” she said. But the day was also tinged by the thought of who she could not share it with.

“I wanted to call Katy and say, ‘You’re not going to believe where I am right now,’” Arons said, “because she should have been there with me.” (Spade died by suicide in 2018.)

She also thought about how to share the experience she had just had with Moore’s clothes with more people.

The Frances Valentine showroom is in what was once called the Beaux-Arts Building, a turn-of-the-century structure overlooking Bryant Park in New York that formerly housed the studio of Jazz Age painter and poet Florine Stettheimer. On a Wednesday morning in late July, Levine and Arons were sitting in the sun-filled showroom at a white table that had been strewn with design sketches and photos of the Mary Tyler Moore looks that had inspired them.

There, too, was The Hat: a squat saucer of wool in concentric rings of black, indigo and forest green, the midnight blue pompom at its center perhaps in need of some fluffing after decades spent in a Manila envelope.

During an interview, Levine spoke about his hopes for the future of Moore’s wardrobe. (Although he could not say precisely how many garments his wife left behind, Levine noted that she had insisted on 100 linear feet of closet space when designing their Greenwich home. “You can be assured that she had that all well filled,” he said.) His wife had not stipulated in her will that anything in particular be done with her clothes, but Levine said he would like to see them end up at a major institution, perhaps in a permanent installation. Everyone seems to agree that The Hat, in particular, is a museum piece.

It’s fair to say that the search for a forever home has gone more slowly than they expected.

When Levine and Arons reached out to the Fashion Institute of Technology, Valerie Steele, director and chief curator of the Museum at FIT, told them that her museum was “not the right venue to accept MTM’s garments,” Steele later recounted in an email. “It’s not our mission.” (She suggested that they try the Museum of the Moving Image, in Queens, or the Paley Center for Media instead.)

Dini von Mueffling, a publicist working with Arons, said one of the main hurdles had been the realization that at top-tier institutions, major exhibitions were often booked two to five years in advance. “Which, maybe it was all a little naive of us to be like, ‘We’re sure they’re going to want it right away — it’s Mary Tyler Moore!’” she said.

Naivete, or optimism? Levine said he recognized elements of his wife’s exuberance in Arons’ own “positive, positive energy.” That might have made it easier for him to throw open the doors of his wife’s closet to someone he had met in person only once before.

“What else was I going to do?” he asked. “If you thought of what’s the best thing that I can do with all these things of Mary’s, it was for me just to share them, because it’s a way to share her and to have the world know another thing about Mary.”