I'm filing married, separately. Spouse is not a U.S. citizen, has no U.S. income. No SSN/ITIN and we are not filing for one. How do I file my return? (Form and address?)

I'm looking to find out what to put on the form for the SSN (Turbotax keeps giving me an error if I leave it blank). If I can e-file that would be ideal, but if not, where do I send the return to? Is it the same address for both the Fed/State return?