Do identical twins have the same fingerprint?
Identical twins have, despite the name, neither identic fingerprints nor identic genetic fingerprints.

Fingerprints: According to the papers listed below the fingerprints show higher similarities (the "structure" is the same), but they can be distinguished and are not the same.


On the similarity of identical twin fingerprints
Can identical twins be discriminated based on their fingerprints?


Genetic Fingerprint: Although identic (or monozygotic) twins share the same DNA, they are not the same and can still be distinguished with a DNA fingerprint, if enough regions are analyzed. The difference comes from small mutations (so called "single nucleotide polymorphisms", one base mutations) which occur in each of us individually. The other difference comes from epigenetic modifications of our genome (basically adding methyl groups to our DNA) which are also not the same between identic twins (there is an interesting video on this on Youtube). However, when using standard forensic kits it is usually not possible to discriminate between identical twins. Differences are detected with whole genome sequencing.

Have a look at these publications:


Identical Twins' Genes Are Not Identical
Finding the needle in the haystack: Differentiating “identical” twins
in paternity testing and forensics by ultra-deep next generation
sequencing
Epigenetic contributors to the discordance of monozygotic twins.