A new company called SheTaxis is based in New York City and provides taxi rides to women, by only female drivers. This is to appeal to women who prefer to be driven by a woman for safety or religious concerns.
There are questions of the legality of such a service. First is the issue of only providing services to women. New York State law prohibits denying customers on the basis of their sex. As such, SheTaxis could face legal ramifications from only picking up female customers.
The second legal issue is that of only hiring female drivers. Employment laws generally prohibit employers from hiring solely on the basis of sex, unless it is a type of position where only sex is able to perform the role. It is not likely that this would be deemed one of those situations.
For more information on SheTaxis and their potential legal issues, see this article: http://blogs.wsj.com/law/2014/09/08/new-car-service-app-for-women-raises-legal-questions-say-experts/