As a native of Southern California (where the modern usage of "dude" originated), and having used it frequently since the inception of that modern usage (with the proper intonation, inflection and emphasis, and within the proper context), I can state without reservation that "dude" is not proper if applied to females. While some have used the term "dudette", that usage has never been widespread. The proper feminine counter to the masculine "dude" is "chick".
That's correct- the classic, simple, "chick". As in "dudes 'n' chicks".
"Dude, you gotta go to my party- gonna be lots of chicks there, man!"
"He's a cool dude."
"She's a cool chick."
An alternate which has found broad acceptance in some contexts is "babe".
"Dude- we need to find some babes to go to the beach with us."
So sayeth the lxdude. Santa Monica born, SoCal raised.