DNA profiles can be used to determine whether twins are monozygotic (identical) or dizygotic (fraternal).
Each parent will pass on one allele (genetic type) to their child and combined these then constitute the DNA profile for the child. If twins are identical, they are likely to have identical DNA profiles. If they are not identical, they are expected to have the same genetic makeup as siblings born at different times, ie. fraternal.
Please see our Peace of Mind DNA testing (non legal) link for more information on how to proceed with Twin testing.