Here's the law and it's a federal crime.
http://www.legion.org/legislative/215862/stolen-valor-act-2013-signed-law
Stolen Valor Act of 2013 - Amends the federal criminal code to rewrite provisions relating to fraudulent claims about military service to subject to a fine, imprisonment for not more than one year, or both an individual who, with intent to obtain money, property, or other tangible benefit, fraudulently holds himself or herself out to be a recipient of:
a Congressional Medal of Honor, a distinguished-service cross, a Navy cross, an Air Force cross, a silver star, a Purple Heart, a Combat Infantryman's Badge, a Combat Action Badge, a Combat Medical Badge, a Combat Action Ribbon, a Combat Action Medal, or any replacement or duplicate medal for such medal as authorized by law.