First of all, your question isn't can the person be charged twice, but can they be charged at all. I say that because the State failed to prosecute. To answer your question: yes, both the state and federal governments can charge a person with substantially the same crime.
The act of doing so is not double jeopardy, but there are guidelines for when it should and should not be done. In your case, it seems unlikely the federal government will pick up a charge the state declined unless it involves/violates a substantial federal interest, and possibly the USPS involvement will constitute that element.
Contact the local United States Attorney's office and see if they're interested in your case. Good luck.
I respectfully disagree with the first answer given. I suggest you go to the Postal Inspectors and lay out your case and see what they will do. Often they will pursue something of this nature quite strenuously. I'm not so sure I would go into all the details about whether the state attorney declined to pursue the matter. Simply let them know what she did and ask them to investigate her actions.
The simple answer is yes. A person can be tried twice for the same act, once by the state and once by the feds. Double jeopardy does not apply because they are separate sovereigns. The state can prosecute the violation of a state crime, and the feds can prosecute the violation of a federal crime.
In some states, it matters in what order this happens. In New York, for example, the state cannot prosecute someone for the same act if the feds went first. But the feds are still free to do it if the state went first. New York gives greater double jeopardy protections than the feds do.
This is not legal advice, and neither creates nor implies an attorney-client relationship.