I did a bunch of searches on Google, and it all seems to go back to a single article in "Iran Focus". I don't know anything about this group, but there is nothing in "Snopes" that says this is an Urban Legend either.
I did find one exception, and it had a little more detail to the story. Still news out of this part of the world is sketchy at best, and perhaps always will be.
The additional article is posted below;
http://www.wifp.org/feministactivism.html#anchor2230084
A 16 year girl hanged in public for having the courage to defend herself in court
Boston, MA - The Women's Forum Against Fundamentalism in Iran (WFAFI) has just been informed that a 16 year old girl, Atefeh Sahaleh Rajabi, was hanged in public on August 15, 2004. Atefeh as hanged in her home town of Neka in northern state of Mazandaran, Iran. She was charged for having an unlawful relationship with a young man.
Despite her family's efforts to obtain a lawyer, Atefeh was denied one by the order of clerical judge. In her own defense, she told the judge, Haji Rezai, that he should punish the main perpetrators for moral corruptions and not the victims. Atefeh was condemned to death by both local clerical judge and Iran's Supreme Court in Tehran. The young man involved in the act only received 100 lashes and walked away free.
After her execution, the local clerical judge said her punishment was not execution but he had her executed for her "sharp tongue". Atefeh was given a more severe punishment because of her gender and courage to talk back to the fundamentalist rulers in Iran's court system. The charges against her were unfounded and the court had no proof of the young couple's relationship.
WFAFI condemns this misogynous act by Iran's fundamentalist rulers and the clerical judges. Even though Atefeh was denied a lawyer for her defense and thus had no fair trial, she was punished for defending herself so courageously.
WFAFI holds the leaders of Iran's fundamentalist regime responsible for Atefeh's murder. Those who commit such crimes against women should be brought in to justice. Violence against women in Iran is institutionalized and Atefeh's case should not be forgotten. We call upon all women's rights activists and human rights advocates to support the Iranian women in their struggle to end such atrocities in Iran.