Premarital blood tests have been used to check people getting married for syphilis, rubella, HIV and sickle-cell anemia. The objective of such tests was to ensure the infected person got treated prior to infecting his or her partner or child. In the United States, premarital blood laws were enacted during the 1930s and 1940s when syphilis was considered a potential public health concern.
Premarital blood test laws were written during an era when premarital sex was largely frowned upon, and the legislators writing those laws probably assumed that most sexual encounters happened within the confines of marriage. In contemporary culture, sexual encounters commonly take place both within and outside the bonds of marriage, making these tests largely irrelevant from a public health perspective.
Only the District of Columbia requires premarital blood tests for both partners; however, Montana requires females to get premarital blood tests, and in New York, African-American and Hispanic applicants have to get tested for sickle-cell anemia.
The reason Montana may still test its female residents is related to that fact that these tests often screened for rubella. Rubella can be deadly if passed from a mother to a fetus; however, even women in Montana can opt out of the testing with a waiver from a doctor.