Final answer:
DNA analysis is the tool likely used to match skin residue under Mary's nails to her husband, providing evidence for the investigation through specific DNA matching techniques.
Step-by-step explanation:
The tool most likely to have helped investigators determine that the skin residue under Mary's nails was from her husband is A) DNA analysis. DNA evidence is very specific to individuals and can be retrieved from body tissues such as skin. Investigators would extract the DNA from the sample, amplify it using Polymerase Chain Reaction (PCR), and then use techniques like gel electrophoresis to compare the DNA sequence against samples taken from the husband. Similarities in DNA sequences provide conclusive proof of identity, which would be critical in such a forensic investigation.