His Wikipedia article says that he's running. I don't know jack about him to say if it's right or wrong.
Some guy with an opinion who found his way to Wikipedia wrote:
In 2006, the Associated Press (AP) reported that Richardson informed party leaders that he intended to run in the 2008 U.S. presidential election.[14] In early December 2006 Fox News claimed that Bill Richardson told them he would run for President,[15] but Richardson said he would actually decide in January 2007.[16]
On Sunday, January 21, 2007 Richardson announced that he has formed a presidential exploratory committee.[17] Richardson joins a diverse field for the Democratic nomination which already includes Senators Barack Obama and Hillary Clinton. While Senator Obama would be the first African American and Senator Clinton would be the first woman, Richardson's own background would make him the first Hispanic to earn a major Presidential nomination.