Yes and no. A vampire still has the ridges and whorls at the ends of her fingers that constitute “fingerprints,” but her dead body does not secrete the oils that leave such telltale marks behind. This means that, while the character doesn’t leave normal fingerprints, her fingers will still leave their unique marks in, say, piles of printer toner, coagulated honey, dust on a computer monitor, etc. Firing a gun does not leave enough powder behind to have to worry about fingerprints, though cordite will stick to a vampire’s hands for a few nights (as it would for a mortal), which may identify him as having used a firearm to forensics experts.