Usually, if you want to remove PMI prior to the regularly scheduled fall-off, you will need to pay for a new appraisal. The reasons for this are:
- (This point is strictly conjecture:) From the bank's point of view, requiring this extra hoop to jump through means less people will do it and/or wait longer before they do, leading to slightly higher profit for the bank.
- Every jurisdiction differs on what time period the county appraisal covers. Many locations appraise for tax purposes based on the value of the home in the previous year, or the average of multiple previous years. To remove PMI you need an appraisal based on now.
- Most of the time, the appraisal for tax purposes is typically lower than the market value. I suspect this is purposely done to lesson the number of complaints and appeals the county would have to deal with, all of which are expensive and time consuming to respond to.
The good news though, is based on point #3, if your county appraisal is leading you to believe PMI can be removed now, then it's very likely that a market appraisal will be even higher. The exception to this is in an economic downturn where property values are drastically falling, but I doubt that is the case in most places in the US (as of today's date).
All that being said, the real answer is lender specific. I've heard of one lender actually using the Zillow stated value for determining whether to drop PMI.