Ann Coulter and Piers Morgan have testy exchange on "Piers Morgan Tonight"

(CBS) On "Piers Morgan Tonight," talk-show host Morgan asked guest Ann Coulter about her personal life. Then things got interesting.

She demurred on answering most of the personal questions he posed Tuesday night on his CNN show.

"Engaged three times, you're 50 in December, are you?" said Morgan at the beginning of the clip. "Seems to be..."

(Scroll down to watch video.)

"I don't talk about either engagements, Social Security number, age or anything else personal," Coulter answered.

Morgan followed up with a question about whether Coulter had ever listed her age incorrectly on an official document.

"There are apparently more than one Ann Coulter in this country," she said. Later she added, "I think like most public figures don't talk about anything that wouldn't...that you would not want the most dangerous stalker to know or have so I will not be answering private life questions. That's why we call it a private life."

Morgan wasn't having it. "You're an agent provocateur."

The two talked over each other for a few moments and then Coulter said, "I write. My writing is interesting," she said.

"You're very personal about everybody else."

Morgan asked if he could throw some hypothetical questions at her but they quickly got into what Coulter characterized as the greatest hits - statements Coulter has made that have been called controversial. For someone who talks a lot about the personal lives of other public figures, you'd think she'd be more open about her own.

Watch the video below or here.