I don't know the details of Maryland law, but typically, state taxes have provisions to file as a "resident", "non-resident", or "partial-year resident". Sounds like for 2014 you're a partial-year resident of both Maryland and New York.
Maryland does indeed have this concept. See:
How much tax Maryland will claim you owe them depends on the details of their tax laws. If you simply moved from one state to another and didn't maintain any residence in the old state -- you don't still have an apartment there or whatever -- it's usually relatively simple: I think for most states, you'd have to pay taxes on the income you earned while you lived in that state. Things get more complicated for people who have two homes, like college students who worked in another state while attending college, people who have two houses and travel back and forth, etc. It can get especially complicated for people who live in one state and work in another, like if you live near the border.
If you earned no income in Maryland in 2014, you probably won't owe any tax, but you probably will still have to file a return. At the least, it will save you from the state wondering why you just quit filing tax returns and auditing you. It may be legally required.