VIDEO: Penelope Cruz Shuts Down Letterman Over Engagement Rumors

Nov. 18 2009, Updated 9:55 a.m. ET

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We're not sure if Penelope Cruz is engaged to Javier Bardem. And her appearance on The Late Show with David Letterman Tuesday night did very little to clear things up.

When the 35-year-old Broken Embraces star -- who wore a sapphire and diamond sparkler at the film’s premiere last month -- was asked by the Indiana funnyman if she had plans on tying the knot with Bardem, 40, she chose to keep her personal life just that: something personal.

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"I don't feel comfortable talking about my private life in public," Cruz, who is notoriously protective of her privacy with the media, told Letterman. "I've been here a few times with you, you know I'm tough. One thing I don't do, I don't lie about my personal life. It's sacred to me. It's my life. But I don't give details about it because I am allergic to that."

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Letterman continued to cajole the beautiful Vanilla Sky star, asking "So you know, but you don't want to tell me?"

Cruz said, "I know, but I choose not to share some things!"

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