UPDATE:
Athens, Ohio is in Athens County. Jane Doe resides near Slade, Ohio which is in Athens County. It is a separate City and County government. The Athens County Prosecutor is Keller J. Blackburn at 1 S. Court Street, Athens, Ohio 45701. He and his staff are the public prosecutors for felony cases and up. On the federal level, an OOS bad check over $500 is considered a felony. However, each state has its own public prosecution regulations and they are different from state to state.
I have talked directly to the public prosecutor in the jurisdiction where Jane Doe is located. The jurisdiction for an OOS bad check can be where the check was tendered or where the check originates. Mr Blackburn's office referred me to the City of Athens prosecutor's office. The City of Athens is the public prosecutor in the jurisdiction where the check originated. James Stanley prosecutes for both City and County of Athens, Ohio. In this jurisdiction the subject circumstances would be prosecuted as a misdemeanor. In addition, while Jane Doe would get a dose of punishment, the prosecution would not nessasarily result in the payment of the amount owed.
The other option is to pursue a civil action against Jane Doe but that would involve travel, time, effort and fees. With only $650 outstanding, may be a losing proposition.
Slick: I did not research pursuing it in the federal system as a result of statutes involving interstate commerce. But it is likely they would refer you to a local prosecutor according to a district judge I spoke to.
JSCATTLE: This does not rise to the threshold of a criminal charge. The circumstances you mention involved more money or other actions of a more criminal nature.
D2CAT: I had a personal situation on EBAY many years ago much like yours with the clock. I sold my son's gaming station on EBAY. The buyer paid with credit card. As soon as she got the item, she went to her bank and filed a stop payment on the item saying it was broken. It was weird, one day my paypal account was credited; the next day it was debited for the same amount. EBAY refused to do anything.
I sent her a letter, very carefully worded. I said, "Lady, I would never have the nerve to do what you are doing. I knew a guy who went half way across the county to settle an issue over $10. Some people are extremely emotional over being cheated. I would be afraid I would walk out to get in my car one morning and the person I cheated would be standing there to greet me." I got paid.