No refinancing has nothing to do with your Property Value.
Trust you are looking into Refinancing again as rates since May have come down even more.
Two great banks are http://www.amerisave.com, http://www.provident.com .
The best part of Proposition 13 were and still are:
1. It restricts annual increases in assessed value of real property to an inflation factor, not to exceed 2% per year.
2. It also prohibits reassessment of a new base year value except upon (a) change in ownership or (b) completion of new construction.
Refinance your loan is changing a lender who you borrow money from.
Your assessed value with be the decided by Santa Clara County tax accessor which will not have anything to do with your refinancing. Now is one of the lowest interest rate for 40 years. If you can qualify a new loan, you should do it. If your assessed value is higher than Market value, you can appy to county to reassess your property value.
Your assessed value after a reassessment shuld be equal to teh market change in you area whether prices have gone up or down.
I hope this helps