Technically, you are required to file tax returns in both states, but "nobody" does. See http://money.cnn.com/2013/06/28/pf/taxes/business-traveler-tax-threat/
Both MD and NC will tax that 48 day income, but NC will give you a credit (or partial credit) for what you pay to MD. For most people, it comes out even and that's why they don't bother filing another return.
As to withholding, that's up to your employer. If he withholds MD, then you will have to file an MD return.
