If you have entered Form 1098-E or Form 1098-T on your tax return in TurboTax, these entries will flow over to your state tax return, if your state allows for a credit of either of these.

Please Note: Not all state allow a credit or dediuction for these.

For an accurate answer, you need to identify the state.

My experience, with a handful of state programs, is the opposite.  The 1098-T and 1099-Q do not flow to state. Additional entries are required.

The 1098-E is reflected in the the federal AGI. If an addback is required, that probably is automatic.