Legal Question in Business Law in Ohio

Whether or not you are incorporated has no relevance on if the city can prohibit you having a pot bellied pig - or any other type of animal for that matter - on your property. One of the functions of local government is to protect the public health, and they generally have wide powers to do so. If they can make a case that it is in the interest of public health to prohibit pot bellied pigs within the city limits, that kind of law is usually upheld.

The only other issue would be whether they are applying the law equally to everyone. Does the town prohibit everyone from having pot bellied pigs, resident and business alike? Or are they selectively applying it and choosing some people/businesses who can have pot bellied pigs and some who can't? Are they are just telling you that you can't have the pigs, while others can? If it is the case where the town isn't applying the law equally, then you might have an issue.

While it might not have been the answer you were wanting to hear, hopefully that helped. Good luck.