You generally only claim an itemized deduction for mortgage interest paid on your principal residence (and a second home) on Schedule A of your federal income tax return, on Line 10 if reported to you on Form 1098, or on Line 11 if not reported to you on Form 1098. Most state returns do not include a similar deduction for home mortgage interest.
The tax systems are separate and distinct - federal under the IRS, and state, under the respective state's department of revenue - it is possible that your state allows for a home mortgage interest deduction on the state return, even though the IRS permits such a deduction on Form 1040 Schedule A.
TurboTax automatically transfers data from your federal return, which you entered in the Federal Taxes section.
You should always try to ensure that you enter your data, and answer the program interview questions as accurately as you can, so the information flows accurately into TurboTax State.
Please note though, as mentioned above, that each state has its own rules with respect to taxation of income and allowable deductions and credits.