Hey, Jeff.
As you can imagine, most out buildings without electric service are built without a permit or inspections. This is not ok, but it happens all the time. I recommend against it. It just takes one anonymous call from a neighbor and you're in the soup.
So, start by checking out teh Hamilton County Building Department web page at:
http://www.hamiltoncountyohio.gov/hcbi/default.asp
Then, figure out whst jurisdiction you fall under and go from there. If its one administered by the County, like Scot says, go to zoning and talk to them about what you're doing. Find out the rules. Zoning is in the County Admin Building on the NW corner of Court and Main.
Hamilton County inspects the footers (I think) even on outbuildings, so you want to start off right. Of course, if you have electric, you need an inspection to connect service.
So you might as well comply with the whole thing. Remember that they charge you for the permit based on the cost of the work, so you tell them you are doing all the work yourself and you're gonna spend about $1000.
Good luck!
PS, I have some junk to bring over too!