While it is preferred that you use an employer's state ID number if you have one, it's not essential if you don't. The only truly indispensable elements on a W-2 for income tax filing purposes are your employer's federal EIN (Employer's ID number), your own Social Security Number (SSN), and your actual wage data.
See additional information in the thread found in the link below:
I don't have my employers state ID number
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