If the State Employer ID is different in TurboTax, yes you should change it to match what is shown on your form W-2. Follow the steps below.
1. Sign into your Online account and select Take me to my return.
2. Select Federal in the left side panel.
3. Next select Income & Expenses at the top of the screen.
4. Scroll down to Wages & Salaries (Form W-2) and select Show more, then select Start/Revisit.
5. Select Edit next to your Form W-2
6. Scroll down to State & Local Taxes. Then make the correction in the box that says Employer's state ID Number.
7. Follow the onscreen instructions to continue your tax return.