The general answer to your question pre-2018 tax filing was "Yes". You could claim the standard deduction for the Federal and itemize for the State.
However, as of 2018 because of the tax reform laws, the answer is "Maybe." You will have to check your state requirements to see if it is allowed in 2018. Some states allow the differing methods and others do not.
The TurboTax program should allow you to itemize your deductions if it is sanction by your State.
I have attached a link to Publication 936. It is 2018 Publication 936.