Quit Claim Deed Taxes

I am in the process of buying my brother through an act of renunciation of claim. Just curious to know how I can go out to re-evaluate my property tax.

The house was purchased in 1999, so that the value is significantly lower than it is today.

According to local practice, you probably can not. Some shipments may be subject to reassessment and if yours is not one of transfers excluded, the value will be reassessed.

Check if this procedure is exempt, as is often where some of the other acts in the title. If not exempt, it is based on the actual purchase price, so if less is good.

If the value is less now, would be a tax assessment down not result in less property tax payable on the property?
What am I missing here?