Your employer normally would withhold from the state in which you live and the state box on your W-2 (Box 15) would indicate a two digit state code (e.g., AL for Alabama, CA for California, etc.), unless your home state and work state don't reciprocate with each other. I would suggest that you contact your employer's HR or Payroll departments or payroll provider ASAP. If your employer forgot to enter it, which is unusual, I believe the IRS wouldn't have accepted it, but I could be wrong on this part.
You can get an automatic extension from the IRS, if you need more time to get a corrected W-2 from your employer. Type "extension" in the search box in TurboTax (without quotes).