Zillow gives the year the Tax assessment and the Assessed Value of the home that year. It also provides a link to the county assessors website. Basically this means that you have to find out the Mill Levy amount and then calculate the monthly or yearly taxes from that number. In Colorado this is area by area levy found on the county assessors website, so it may differ in different parts of your city, state and much different between states.
To calculate the property tax, the authority will multiply the assessed value of the property by the mill rate and then divide by 1,000. For example, a property with an assessed value of $50,000 located in a municipality with a mill rate of 20 mills would have a property tax bill of $1,000 per year. ~Wikipedia
Seems like Zillow has this info on their website so they should be able to open that up in their API, but sadly they don't. Makes for a lot of extra work! Good Luck