For 2017, I do not owe any tax to the State of California. How should I file my taxes? Online or by sending hard copies of forms?
Also, do I need an ITIN for this?
As per the comment above, if your income is above the threshold, then you need to file, even if you don't owe anything. You need to assert that the numbers in the forms are correct, i.e. what your income really was, what your deductions are, etc. You signing and submitting the form is your telling the government that you think those numbers are correct. If those numbers aren't correct, your filling out that form lets you tell them what you think the correct numbers are. Even if after that form is completed, it really does actually balance out to zero, you still need to submit the form to attest that you think that it balances to zero.
As for how to file, paper or electronically is your choice. And as to whether you need an ITIN, the answer is undoubtedly, yes. Again, those numbers in those forms have to be tied to some for of identification. That is your ITIN. Whoever was paying your income should have demanded that number in order to properly credit your income to the right person to the government.