Since you are a Maryland resident you have to pay Maryland tax on all your income, no matter where the income is from. If your employer does not withhold Maryland tax, you have to make estimated tax payments to Maryland during the year. If you don't, the "challenge" that you will come across is that you will have a huge payment due when you file your Maryland tax return at the end of the year, plus a penalty for not having paid anything during the year.
New Hampshire has no income tax on wages, so you do not have to worry about New Hampshire tax, and you do not have to file a New Hampshire tax return.
