I would suggest you check out
http://www.ohsaa.org (Ohio State HS Athletic Asso.) and click on OFFICIALS. Click FAQ and it explains the steps necessary to transfer from another state. Looks like they have a formal process required.
If you are a member of IAABO you may want to contact the board there (or if you want to join it):
LAKE ERIE DISTRICT BOARD (55)
TERRITORY -- CUYAHOGA, ASTABULA, GEAUGA, LORAIN, STARK AND MEDINA COUNTIES
PRESIDENT -- CARL JORDAN
INTERPRETER -- TOM TOOHIG
SECRETARY-TREASURER -- CHUCK GRIMM, PO BOX 360711, STRONGVILLE, OH 44136
EMAIL:
[email protected]
Either of these options should point you in the right direction. Good luck.