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Have you asked them?
Phone:(419) 523-4628
Don....
Are the fairgrounds public access? Or locked up when not -in-use ? We had a particular fairgrounds near us, that was, like many, locked up when not in use. However a local md'r here was a member of the VFW. And they held their monthly meetings in one of the community rooms located at the fairgrounds. So he wised up, and .... knowing the gates opened an hour before the meeting each month (to allow the early arrivers to set out chairs, start brewing the coffee, etc...), he'd detect for that one hour, out yonder on the hither portions . No one ever bothered him, and he found a lot of silver coins that way. He didn't ask anyone (as his presence there was not un-authorized, dis-allowed, nor was it "trespassing", nor was there any express/specific "no detecting" rule on that location, etc....
If the OP feels he MUST call someone there, then he should phrase it like this: Where can someone avail themselves of the rules of use of the fairgrounds. Like is there something at the turn-style entrances listing the rules? Ie.: no alcahol, no dogs allowed, etc.. And then if it's city property (and if you're of the skittish worrisome sort), you can go a step further and see if your city codes have any municipal wide "no detecting" (which I HIGHLY doubt).
Because the danger of just calling up some random pencil pusher at a fairgrounds phone #, is you might just get a "no", simply because someone envisions geeks-with-shovels. Whereas, fairgrounds get detected all the time. Same psychology as those who have gone to city halls around the USA and found themselves "no's". Only to find out later that the parks in that city get detected routinely, and no one ever had a problem before.