If neither party to be married is a resident of the county in which the ceremony will take place, Maryland law allows application for a marriage license to be made by mail. Contact the Clerk of the Court for a Non-Resident Affidavit form.
Take the form to the Clerk of Court or comparable official in the county in which you reside. Complete the form in the presence of that official, have that official sign at the appropriate place, and mail the form with a money order or cashier's check for $60, payable to Clerk of Court, to the Washington County Clerk of Circuit Court. Comparable officials would include: Clerk of a Court; Recorder of Deeds; Prothonotary. A Notary Public is not a comparable official.
Note that this provision is a Maryland law. Clerks of Court in Maryland counties will provide this service. Officials in other states are not bound by Maryland law and may not provide this service. Check with the official well in advance of your wedding date to be sure. If no comparable official will provide the service, one of the parties will have to make application in person in Washington County.