Republican-leaning group American Crossroads in its own online video also plays on the Tennessee angle and ties her closely to President Barack Obama, who is unpopular in Kentucky.
University of Louisville political scientist Laurie Rhodebeck said Judd certainly wasn't frightened out of the race.
"She doesn't strike me as a shrinking violet," Rhodebeck said. "I think the real issue would be how much disruption she wanted in her life. This was the kind of thing that she would have to throw herself into 100 percent in order to make it worthwhile."
Judd and three-time Indianapolis 500 winner Dario Franchitti separated early this year after marrying in his native Scotland in 2001.
Judd's decision not to enter the race leaves the Democratic Party in search of a candidate. Many of Kentucky's top Democrats, including Beshear, have said they won't run. However, a rising star within the party, Secretary of State Alison Lundergan Grimes, hasn't ruled the race out. Grimes declined comment Wednesday evening through her spokeswoman, Lynn Sowards Zellen.
Associated Press writer Janet Cappiello contributed to this report.