My federal return was filed by a CPA. Can I e-file the state return through Turbotax without the federal return? If not, then I have to mail it on paper?

No .. it must be mailed.  But why did the CPA not also efile the state return ?    Why do you want to enter in the entire federal return to populate the state yourself ?   Seems like a lot of unneeded work. 

When you use TurboTax the information flows from your federal return to the state return.   You have to prepare a federal return first in order to prepare a state return.   You cannot prepare a "stand alone" state return.   And you cannot e-file a state return using TurboTax unless you have also successfully e-filed a federal return using TT.

 

 

 

 If you still need to prepare the state then use the information from the federal return you have to prepare the state yourself using the state's forms from the state's tax site, or have your CPA prepare the state for you.

 

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573