My federal was offset and I received an advance from Credit karma. Will they take the fees from my state refund

If your federal tax return was subject to an offset, then unless that completely satisfied the obligation for which your refund was offset, then your state refund will also be subject to an offset.  If this is the case, then you will have to pay Credit Karma out of pocket.

I had a prior tax obligation with IRS and my obligation was paid in full with my the federal refund. My question will the fees be withdrawn from my state?

No ... Credit Karma will not be able to attach the state refund.   You are responsible for paying back the advance as you agreed to do in the document you signed.  They will probably mail you a bill and payment instructions.