Tax filing

I have been asking my employer why my state of residence taxes haven't been filed.  Upon taking the job, I filled out all of the paperwork and even asked about Md taxes. They told me they would take care of it. I have just found out that they have not been paying Md. taxes nor are the taxes taken out of my check. Instead I have been paying VA taxes, even though I have never lived there. They said I would need to file for a VA non resident and owe MD taxes. Is this my responsibility or is it on them to file the taxes correctly?