Their birthplace has often been reported as Midland, Texas. That’s the hometown of the twins’ mother, Laura Bush, and it is where Laura and George W. Bush were living in 1981, when the twins were born.
But because of difficulties with the pregnancy, Laura Bush traveled to Dallas to have the twins. We ran onto this fact some time ago in a transcript from the CNN show Inside Politics. The show aired on 19 September 2000, and included a clip of George Bush talking to Oprah Winfrey about the birth:
…[Laura] became ill, she got toxic — toxemia and so. We had to move from out of West Texas and she moved to the hospital in Dallas and she got on the airplane. She said, these babies are going to be born healthy.
In 1981, 2 famous births occurred at BUMC: Laura and George W. Bush became the proud parents of twin daughters… Multiple births are considered high risk, so the neonatal facilities and specialists available at BUMC made it the logical choice for this special delivery.
(Note to college buffs: Yes, Baylor University is in Waco, Texas, but the medical center is in Dallas, 100 miles north.)
Given these sources, it seems fair to say that the Bush twins were indeed born in Dallas.