Do Maryland non-residents need to file state tax? (living abroad in Europe full time and didn't earn any income in Maryland)

No. Non-residents do not have to file an MD state return if they have no Maryland sourced income. 

Residents are individuals:

• Who are domiciled** in Maryland for the entire year, or

• Who have a permanent home outside Maryland, but who maintain a place of abode in Maryland for more than six months of the tax year.

The individual must file a full-year resident return if physically present in Maryland for more than 183 days.

Nonresidents are individuals who are not residents of Maryland during the year. 

**Domicile is the place an individual establishes as his or her permanent home and the place to which he or she intends to return after any period of absence. A domicile, once established, continues until a new, fixed, and permanent home is acquired.