Property taxes have nothing to do with whether or not you are a US citizen - property taxes are assessed against the property.
Typically the local tax assessor gives each property a value, called an assessment, based on 2 things - land and improvement (what's built on the land such as a house). Based on the total assessment of all properties in that town, a factor (called a tax rate) is established to raise the money needed to fund the town's budget.. This simple explanation should give you the general idea of how this works.
You should call the tax assessor of the town you're considering to discuss this fully and to learn the schedule for the next tax re-valuation. Periodically towns re-value all properties and this can significantly affect a home's tax burden, I would also suggest that you consult with a real estate attorney on this as well.