ja_mageia

As a matter of law, yes, because constitutionally there is no double jeopardy or double punishment. Both the Federal government and a State may prosecute someone for the same conduct.

However, as a matter of policy, the military usually does not punish someone for an offense for which they have already been tried by a State court. The military can enter a civilian conviction in the member’s personnel record, suspend various privileges, require alcohol or drug screening, etc. (These are administrative matters and are not considered disciplinary or criminal penalties.)