Yes, if you had the same employer last year you can use the same number. Only your employer can provide you with your employer's state ID number (and explain why it's not on your W-2.). If you do not have the EIN on your W-2, you can call your employer and ask for it.
Good News! Your e-file return will still go through just fine, as long as there are no other errors on your return. Your state department of revenue will be able to easily identify your employer from their 9-digit federal EIN, so the state ID number is a little redundant anyway, but is still a way that your state tracks employers in their internal state computer system.
However, the state employer ID number is really only a bureaucratic convenience for your state's department of revenue; it's simply not an essential element to the correct filing and processing of a valid personal income tax return (either state or federal).
