In California, it's the Mills Act. In Oregon, it's the Special Assessment of Historic Property Program. In Wisconsin, it's the Supplemental Historic Preservation Credit. In Arizona, it's the Historic Property Tax program.
Whatever it's called, many -- if not most -- states have programs in place to reduce the state property taxes of historic buildings. Of course, with programs administered at the state level, requirements and benefits differ depending on where your property is located. A quick online search that includes the terms "tax, historic and state" should land you in the right place quickly.
Note that these programs are very different in the kinds of breaks they offer. While the previous pages detailed ways to get breaks on renovations, many individual state credits offer breaks on the property taxes you pay every year. Instead of having to spend money to save money, these state programs can help you save money outright.