This is an interesting question, and it applies to all monozygotic twins, not just conjoined. The short answer is: No, they do not have the same fingerprints. For the long answer, and more information about why not, check out my article about Twins and Fingerprints.
Conjoined twins, also known as Siamese twins, are a rare type of monozygotic (identical) twins. Find more answers to Frequently Asked Questions About TTTS. (If you have a question that is not answered here, please e-mail me: multiples.guide@about.com.)

