Employer accidentally withheld income taxes for a state that I don't even work in - now they've furloughed me and I have to file for unemployment

Long story short, I transfered to a new role. I took someone's job that was previously based out of New Jersey. I live in Maryland.

My first paycheck had taxes taken out from both New Jersey and Maryland despite the fact that I exclusively live in and work in Maryland.

I requested that HR correct this and unfortunately with the entire COVID-19 thing going on it's taken them two weeks. Today, I was furloughed and I have a strong feeling this is going to cause a headache when I file for Maryland's unemployment tomorrow.

Does anyone have any advice/tips/etc for this situation?

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