Trayvon Martin's hoodie: Will it go on display at museum?

(CBS News) A museum director at the Smithsonian Institution in Washington, D.C., said she would be interested in acquiring a symbolic and recent piece of American history.

Trayvon Martin's hoodie - the sweatshirt he was wearing the night he was fatally shot by George Zimmerman in Sanford, Fla. - "became the symbolic way to talk [about] the Trayvon Martin case," Lonnie Bunch, the director of the Smithsonian's National Museum of African American History and Culture, told The Washington Post.

As legal proceedings have come to an end, the hoodie is likely back in the hands of the Sanford Police Department and Trayvon Martin's family will be given a chance to claim it.

Wall Street Journal art reporter Kelly Crow told CBS News that, despite the intrigue, it is unlikely that museums will be clamoring over the hoodie, due to the sensitivities surrounding the case.

"I think the art world probably wouldn't be lining up to display this tomorrow because it could be seen as a little exploitative," Crow said.

If put on display at the African American History Museum - which is currently under construction - the hoodie would join a collection that includes the handcuffs used on Harvard professor Henry Louis Gates as well as artifacts belonging to Harriet Tubman and date back to the days of slavery and the underground railroad, CBS News' Chip Reid reports.

"I think museums have always seen it as their mission to chronicle the human experience. Some museums define that in terms of famous paintings and sculptures; other museums define that in terms of artifacts that, you know, sum up the zeitgeist of a certain historical moment," Crow said.

The collection of these kinds of artifacts is on the rise. The Law Enforcement Memorial Fund is building a museum in Washington that will eventually house the car, sniper rifle and other items used by Lee Boyd Malvo and John Allen Muhammed, the snipers who terrorized the D.C. area in a three-week, 2002 killing spree.

And while an artifact from another famous criminal case - the infamous ill-fitting gloves worn in court during the trial of O.J. Simpson - have yet to be displayed by a museum, they were put on display at the Palms Resort in Las Vegas four years ago.

"I think museums should chronicle the whole sweep of history," said Crow. "The bad stuff happened, and it's part of the story, and it should be included."