It all depends on the particular facts and circumstances of your case.
If the case involves multiple victims and a loss greater than $50,000.00 to those victims, it is likely that the matter may be investigated by a federal law enforcement agency (likely the FBI or the United States Secret Service). There are a number of crimes with which you may be charged depending on the nature of the crime. Generally, a federal prosecutor would look to Title 18, United States Code, Section 1028 to determine what criminal statute applies.
In addition to any substantive statute, Congress recently passed a law making Aggravated Identity Theft a federal crime punishable by an additional mandatory term of imprisonment in a federal prison. Pursuant to Title 18, United States Code, Section 1028A, a person convicted of Aggravated Identity Theft faces a mandatory minimum federal custodial sentence of two years imprisonment - in addition to any other sentence imposed by a federal district court judge.
However, all of this depends on the nature of your conduct. I would encourage you to seek legal counsel in your area from someone who has experience defending criminal cases - particularly those involving identity theft.
Generally speaking, cases involving less than $5,000.00 would typically be handled by local authorities including the local district attorney's office.
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