With the update to the Military Spouse Residency Relief Act the spouse can now claim the state of residence of the military member.  Based on what you provided in your post the MW507M is like a W-4 for Maryland state tax exemption for wages.  To be filed annually with the employer by Feb 15.

If the military member and spouse both do not pay Maryland state tax then they would not file a Maryland tax return.  However if state tax was withheld and they would like to a refund then I would file as a non-resident.

If the state the military member and spouse claim as their state of residence requires a return then they must file that return as well.