It used to be. I think it came from the tradition of proving the bride's virginity.
Unless accompanied by a further physical exam, blood tests won't tell anything about a person's virginity or not.
However, and this was not mandatory, but rather dictated by custom, social status and other indicators, sometimes girls graduating from some schools were given a virginity and maturity exam, meant as reassurance for the parents about their daughter's prospects as a future bride.
I read about this being the custom in Germany in certain Catholic schools at least until the late 1930's. In a biography of Eva Braun, (The Lost Life of Eva Braun by Angela Lambert) this is briefly mentioned and discussed as often being customary in the better sort of boarding school. Not only is it a reassurance of a daughter's virginity, but in the case of boarding school pupils, it's also a way of proving that the girls have been properly supervised during their stay at the school, relieving the school of any responsibility for possible negligence on that account.
Aside from Interwar Germany, this sounds like something that families in certain social circles would very discretely insist on in other (European) countries as well, especially where lineage, social standing and class were considered to be of paramount importance when choosing a bride.