Sounds like you'll need to file as Married Filing Separately.
If you are married by IRS standards, you can only choose "married filing jointly" or "married filing separately" status.
Since you have no dependents, you can't file as Head of Household.
Please see the TurboTax blog How to File Taxes When I'm Separated From My Spouse for more information.
You may file as single if you are "considered unmarried" under state law, by reason of a court order of separate maintenance. However, I have never seen a situation where this was actually allowed. I have only researched New York law, and in that state, the situation of being separated under a court order of separate maintenance seems to be a throwback to when divorce was rare and difficult to get, and a separated couple might go to court to get an order that each spouse must be free to live a separate life, and the usual legal responsibilities of spouses toward each other no longer applied, except that they could not remarry. In the modern era, this type of court order is rarely pursued and people just get divorced if they need to, so that in New York, there is no marital separation that qualifies a taxpayer to file as single, if the separation includes court-ordered alimony or support.
I don't know the laws of any other state, so if you felt that you somehow are "unmarried" under state law without benefit of an actual divorce, you would want to get an opinion from a legal expert in your state. Otherwise, you are still married and must file as married filing separately.