Many people think that there is no such thing as Batwoman but there is. In the 1950's Kathy Kane, a circus performer who aspired to be more, came upon an inheritance...making her an instant millionaire. She met with all the socialites in Gotham City, including Bruce Wayne. Yet she was still bored. Then she met the Batman...and knew what she had to do. Donning a costume inspired by the dark knight, she embarked on a career as the Batwoman. After years of retirement, she reappeared when the evil Professor Hugo threatened Gotham City. Here is the tale she appeared in, with Robin and the Batman of Earth-1! As many Golden age characters Batwoman didn't exist in the Modern age at all. The first apperence of Batwoman was in Detective Comics #233 - "The Batwoman" - July 1956.

In 1984's CRISIS Batwoman returned as an Earth-2 Heroine. Same Origin (I THINK?)

"Although his career as crime-fighter is sometimes a lonely one, up till now, Batman has never allowed himself to think of marriage -- for he knew that marriage would not only mean endangering his wife, but would jeopardize his secret identity as well! But, suddenly it happens -- Batman does marry -- and to another costumed crime-fighter -- the glamorous and lovely Batwoman! How this comes about is revealed in the surprising story of...The Marriage of Batman and Batwoman"