It is not currently a crime in New York under state law. There is a bill in place that has been passed by the Senate but not the Assembly (and thus not yet a law): https://www.nysenate.gov/legislation/bills/2015/s5201/amendment/original. If/when it is enacted, it would be a Class E felony (the least serious form of felony), which is 1-5 years in prison. Again, it is not yet a law, so it's not a crime under state law.
It is a crime under Federal law in certain instances: The 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 Medal of Honor (Army, Navy, Air Force, Marine Corps)
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.
Note that it's not enough to simply claim to have received them, but rather to do so with the intent to receive money or property. The previous Stolen Valor Act (much broader, in that it simply made it illegal to falsely claim this at all) was ruled unconstitutional as an infringement of freedom of speech.
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