If you are married, but you file "Married Filing Separately (MFS), your husband does not need to sign that return. If you are considered "Unmarried" your husband does not need to sign the return.
According to the IRS:
"Marital Status
In general, your filing status depends on whether you are considered unmarried or married.
Unmarried persons.
You are considered unmarried for the whole year if, on the last day of your tax year, you are either:
State law governs whether you are married or legally separated under a divorce or separate maintenance decree."
If you are still married, you cannot file "Single". Your choices are married filing jointly or married filing separately.
If you are married, but you file "Married Filing Separately (MFS), your husband does not need to sign that return. If you are considered "Unmarried" your husband does not need to sign the return.
According to the IRS:
"Marital Status
In general, your filing status depends on whether you are considered unmarried or married.
Unmarried persons.
You are considered unmarried for the whole year if, on the last day of your tax year, you are either:
State law governs whether you are married or legally separated under a divorce or separate maintenance decree."