11/17/2009 AT 7:40 PM ET
It’s a question she just won’t answer – no matter how hard she’s pushed. During her Late Show appearance, airing Tuesday night, David Letterman asked the actress, 35, point-blank if she’s engaged to Bardem, 40. “I don’t feel comfortable talking about my private life in public,” she said, laughing.
Letterman pressed and Cruz continued, “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,” she said. “It’s sacred to me. It’s my life. But I don’t give details about it because I am allergic to that.”