Paul condemned the shootings, which included Rep. Gabrielle Giffords among its victims. She remains in critical condition after being shot in the head.
Paul said that though Arizona is only one of three states that allows people to carry concealed weapons without a permit, "I don't think that that plays into this at all. Really, I think they're unrelated."
[TPM SLIDESHOW: Across the Nation, Vigils Held for Rep. Gabrielle Giffords]
He also said that "from a medical point of view, there's a lot to suggest paranoid schizophrenia. That this man was a really sick individual."