I am married but my husband does not live or work in the US. Under what status should I file taxes, i.e. single or married, since he does not have a SSN.

[chhavi-karir]

Turbo tax is not allowing me to proceed with filing unless I fill in his SSN.

[fanfare]

If you are married, you cannot file status Single.

[DanaB27]

You will have to either file married separately or treat you spouse as a resident and file married filing jointly (please see IRS Nonresident Alien Spouse for details for this option).

If you have children living with you then you might qualify to file as head of household. 

If you file married filing separately then you will have to enter the spouse's Social Security number as 999-88-9999 when TurboTax asks about the spouses SSN.  You can only print and mail your tax return, it cannot be e-filed.  When you print the tax return erase the Social Security number for your spouse and manually enter "NRA" for non-resident alien.

Please see How do I print and mail my return in TurboTax Online?