The 16th president's blood is on a strip of a pillowcase in the collection of the Grand Army of the Republic Museum and Library.
Cardiologist John Sotos believes Lincoln had a rare genetic disorder and wants the DNA test to prove his hypothesis.
Sotos, author of "The Physical Lincoln" (Mt. Vernon Book Systems), contends that Lincoln and four members of his family had a rare genetic cancer syndrome called MEN2B, and that he would have died of the disease had he not been assassinated by John Wilkes Booth.
Sotos also suggests that Lincoln knew he was ill and that that knowledge would color his decisions in office - and even his famed quote that he "shall not outlast the Rebellion."
The museum's board met Monday night and rejected Sotos' request to test the pillowcase.
Board President Eric Schmincke says more questions need to be answered about how the artifact will be treated.
He says it's possible that testing will be overseen by the National Museum of Health and Medicine.
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