And if a man shall take his sister, his father's daughter, or his mother's daughter, and see her nakedness, and she see his nakedness; it is a wicked thing; and they shall be cut off in the sight of their people: he hath uncovered his sister's nakedness; he shall bear his iniquity. They include father, mother, step-mother, sister, step-sister, grandchildren, aunt, uncle, daughter in law, and sister in law.
Technically, this does not prohibit marriage to cousins.
people with common grandparents or people who share other fairly recent ancestors).
You can also look it up under "marriage" or "domestic relationships" in the legal statutes for your state (paper copies are found in a state government office).
Now, there may be other reasons that this arrangement is bad.
I would certainly be very uncomfortable with a first cousin arrangement since this would be very close to the biblical prohibition.
For more general information and studies on the effects of blood related unions, visit the March of Dimes Birth Defects Foundation web site.
You say you have a "don't care" attitude, but you are smart to ask about the risks — legal, moral, and medical.