To meet Selective Service Registration or Military Service Requirements for naturalization, one of the following conditions must apply:
If you served in the U.S. armed forces, you must not have deserted and you must not have obtained an exemption or discharge on the basis that you are an alien. If you are a “conscientious objector” (i.e., if you object to military service on the basis of freedom of thought, conscience, or religion), you must be willing and ready to perform non-military service.
Applying for Citizenship
Citizenship after Marriage to U.S. Citizen