February 15, 2015 09:00 AM

Kristina Bumphrey/StarTraks

From her starring role on Sex and the City and innate sense of style to launching her own shoe line, Sarah Jessica Parker is undeniably a fashion icon. But did she pass those genes on to her kids?

“They’re at an age — and have been for many years — where they really have their own identity,” Parker told PEOPLE of her children with Matthew Broderick (son James Wilkie, 12, and 5½-year-old twin daughters Tabitha and Loretta) at the Fendi New York flagship store launch Friday.

“So Sunday through Thursday, the rule is they can wear whatever they want,” Parker, 49, adds. “And if we go to the theater or to the ballet, I get a say. But it’s really among choices that they approve of.”

As for whether they inherited mom’s fashion sense, “It’s not something we talk about.”

Parker — who’s set to appear in the upcoming HBO comedy pilot Divorce — has dished on her kids’ creative sides before, so it wouldn’t be a surprise if the she’s got some trend-setting mini-me’s on her hands.

“They’re all preternaturally gifted artists,” the proud mom told PEOPLE last year. “They probably spend 80 percent of their free time drawing … Every morning before breakfast, we have to drag them away from drawing and painting, even my son. They’re far more gifted than I ever was.”

— Jeff Nelson

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