Yes it is possible. The dual sovereignty doctrine provides that “when a defendant in a single act violates the ‘peace and dignity’ of two sovereigns by breaking the laws of each, he has committed two distinct ‘offenses’ for double jeopardy purposes.” This means that if your conduct violated both state and federal laws you can be charged and convicted in both, or you can be acquitted in one court, and later tried and convicted in another. Double jeopardy only prevents the same court for prosecuting you twice for the same conduct.