The Nine star giggles her way through questions about her baseballer beau

Credit: Seth Browarnik/Startraks; Statia Photography/Getty

Kate Hudson and Alex Rodriguez’s steamy romance is hardly a secret. Aside from countless very-public dates and outings, she spent the summer attending – and being endlessly photographed – at his Yankees games, both in New York and on the road.

But during Thursday’s Late Show with David Letterman, the Nine star, 30, didn’t give in to the talk-show host’s nosey questions about her relationship with Rodriguez.

When Letterman opened up the questioning with, “You’re a big Yankees fan, and you’re friends with Alex Rodriguez,” Hudson giggled sheepishly and said, “Yeah, he’s a friend of mine. Nice guy.”

RELATED: Kate Hudson Brushes Aside A-Rod Rumors
So how did she and Rodriguez, 34, meet? Hudson laughed and responded, “Can’t we talk about the holidays?” Did they spend Thanksgiving together? More laughter. Letterman then prodded, “So is he a nice guy?” Hudson finally caved, saying, “Yeah, he’s a nice guy. You just can’t help yourself! You just can’t! I knew it was going to come at some point!”

And when Letterman pointed out, “His game changed when you started showing up regularly at ball games,” Hudson responded, “It was a really fun summer,” adding that the Yankees winning the World Series – an achievement for which Rodriguez received accolades – “was awesome!”