DoD civilian working overseas, do I file MD state taxes as resident or non-resident?

You actually have (2) really good questions here:  which mailing address to use, and what is your residency status.

As to the first question, you can actually use whatever address you like, as long as you can receive mail there.  That decision doesn't affect your residency for tax purposes at all, so you can think of this choice independently of anything else.  Simply for administrative purposes, if you have a family address in Maryland, that may be easier to enter into the software; and also quicker for the revenue authorities to reach you with any future notices (letters, refunds, etc.), so you could use that one simply as an expediency.  In other words, official mail will simply reach a Maryland address faster than an APO address or a German address.  Someone at that Maryland address (your mother, for instance) could then promptly alert you to the arrival of any government letter or correspondence.

With respect to the second portion of your question, Maryland residency, I've gathered together some materials for you to read.  They can be found at the following (2) Maryland webpages:

http://taxes.marylandtaxes.com/Individual_Taxes/Individual_Tax_Types/Income_Tax/Filing_Information/Determine_Residency_Status/

http://taxes.marylandtaxes.com/Resource_Library/Tax_Publications/Administrative_Releases/Income_and_Estate_Tax_Releases/ar_it37.pdf

My own reading of those materials would lead me, as a CPA, to conclude that you are a full-year Maryland resident for the 2016 tax year.  For future tax years you will remain a Maryland resident, even if living year-round in Germany, until such time as you establish residency in another US state (or if you cease to become an American citizen, and emigrate to a foreign country . . . but that's a drastic step to take to rid oneself of Maryland residency simply for tax reasons).