Yes.  Although it is rare, you can be charged with the same offense or fact scenario in both State and Federal Courts. State and Federal Prosecutors will usually get together and decide whether the case should be handled on the State or Federal level. Many considerations go into this choice including the nature of the crime, the potential punishment, the workload of a prosecutor or agency, and who discovered or investigated the crime.  For example, when cases are prosecuted in both State and Federal Courts for the same conduct, the State would prosecute a larceny and the Federal side would prosecute a tax evasion charge.

Ask your attorney about the Petite Policy, which is an internal Justice Department guide which states that absent compelling federal interests, the Federal Government should not prosecute whenever a State has done so. This is merely a guide; however, it is worth examining if you find yourself in this situation.