An interesting idea, but which Maine tax would apply? I'm not a Maine tax lawyer, but it looks like Maine has plenty of taxes, including a "Blueberry Tax" [1][2], but there doesn't appear to be a general assets tax. Any corporate income from licensing the patent would be taxed just the same as any other income.
Maine's property tax appears to apply only to "real property" (land) and "tangible" personal property [3] ("tangible" property includes tractors, factory equipment, and other things you can pick up and hold --- patents and other IP are "intangible personal property.")
If you think it's a capital asset subject to capital gains taxation, there's usually no tax on that until the gain is realized by sale. I don't know how patents are taxed in states with general ad valorem taxes, but Maine doesn't seem to be one of those states.
[1] http://www.maine.gov/revenue/othertaxes/homepage.html
[2] http://www.mainelegislature.org/legis/statutes/36/title36ch0...
[3] http://www.mainelegislature.org/legis/statutes/36/title36sec...