My dependent's father is claiming her on his federal return. Can I claim her on my California state return?

[Vanessa A]

Who does she live with?  If she lives with you and you are the custodial parent, you can still claim her on the federal return as well,  you just need to mark that the other parent is claiming her.  The only thing the non custodial parent can claim is the child tax credit.  The custodial parent gets the rest of the credits. 

If you do not enter her on your federal return, yes, CA allows you to claim dependents on the state return that you did not on your federal return.