Zoning laws can be VERY quirky, and complicated. Firedrake is correct in what is the 'likely' scenario in most situations.
What is the 'need' of your plotline? It sounds like you have two goals.
ONE - Obliterate the house.
TWO - Insult the neighbors.
I'm assuming this is NOT a real town? If it were, you could go look up the zoning laws - which often vary from neighborhood to neighborhood anyway. Its not a bad idea to do that anyway, just so you'll know what is the standard practice for small towns in that part of Ohio.
Levelling the house, should prove no problem. Demolition permits are usually issued in order to pave the way for new construction - OR to simply clear the lot for sale.
IF your goal is to place a parking lot in the midst of the neighborhood - you'll need to come up with some sort of QUIRKY 'grandfather clause' to the zoning restrictions. This would have to be worked into the plot. Perhaps the swanky neighborhood has a zoning law that allows the 'original' property holders to dispose of their property outside of the zoning restrictions? Maybe the MC house, was the FIRST homestead built in the area - perhaps its the original farmhouse, whose property was later turned into the subdivision that all the swanky houses now sit on? I could see the original stipulations for sale of the property to the developer - saying something like "You can develop the land as a high end neighborhood with zoning restrictions - but I and my heirs have the right to do ANYTHING we want with our house and the lot it now sits on - in perpetuity..." I can see a greedy developer who was dying to get his hands on the farmland agreeing to such a condition. Assuming that by the time the old man died, the development would be built, his profit made, and it would be the problems of the neighborhood.
Which is exactly what you want.
Ergo - its possible to turn the lot into a paved over wasteland. End of story.
OR you could find some OTHER egregious building to put on the lot, if you can't make a parking lot there. Perhaps build a building that is going to annoy the neighbors no end? Some religious commune, some political statement, some sort of 'half way house' that would drive them nuts, and yet serve as a tribute to the MC's own philosophies and beliefs?
Off for coffee now, good luck.