Report: Sarah Jessica Parker and Matthew Broderick Welcome Twins!
A spokesperson for East Ohio Regional Hospital had no comment, but told PEOPLE "everything's good." Reps for the couple could not be reached for comment.
"I'm thrilled for Sarah, Matthew and James Wilkie," Sex and the City costar Kim Cattrall said Tuesday after the babies' birth was reported. "More 'fabulous girls' are joining our SATC family."
The news first broke in April that the couple were adding to their family by having twin daughters with the help of a surrogate mother. Broderick, 47, and Parker, 44, have a son, James Wilkie, 6.
"The entire family is overjoyed," the couple said in a statement at the time.
By May, the big brother was "pretty excited" – and already making a shopping list, according to his father. "He said, 'We have to get a lot of princess toys.' "
Once the pregnancy was announced, friends of the couple said that while the news came as a surprise, it was, in a way, also expected. "They love kids and wanted more," said one friend. "They absolutely love being parents."
Added another close pal: "They are very happy. They've wanted to become parents again for a while."
Parker's Sex and the City costar Mario Cantone told PEOPLE that having daughters was always a dream for Parker, who is known as one of Hollywood's most fashion-savvy stars. "She has definitely wanted to have a girl. She's going to have so much fun bringing the two girls up and teaching them to be young ladies."
Parker has described the surrogate as a strong woman who made "an incredibly generous and gracious choice." Added Parker, "She's made a really big choice to be part of our lives and I think she's an honorable person."