You'd only make adjustments to your California return if you have any income or deduction items that are treated differently between the IRS and federal. TurboTax will automatically make many of these adjustments on your return. For more information on the types of adjustments you could make on your return, you can review the instructions to Schedule CA (California Adjustments).
If you didn't receive a W-2 for your work, you would be treated as an independent contractor for both federal and state tax purposes. At the state level, there usually isn't a difference between how employees and independent contractors are taxed.