I've always used logistic regression when Y was categorical data 0 or 1.

Now I have this dependent variable that is really a ratio/probability. That means it can be any number between 0 and 1.   

I really think "logistic" shape would fit very nicely, but I remember categorical Y was a big deal when proving why MLE works.

The point is, I am wrong using logit regression for this Y or it doesn't matter? Should I use probit instead?   

Am I committing a capital crime?