Do I have to file my state income even they are not taxable?

Which state do you live in and why is it not taxable?

In general, no, you do not need to file a return if you have no income to report, however, some states may require you to file depending on the type of income and why it is not taxable. 

And for some states...if you are required to file a Federal tax return, they require you to file a State tax return too...even if zero owed.