Welcome to California!
Yes, you pay property tax every year. Fortunately the sales tax (hidden as the use tax on out of state purchases) is once and done.
Property tax is approximately 1% of assessed value (which is supposed to be actual market value). I think the actual tax rate varies a bit from county to county. I think I pay slightly more than 1%. (Alameda County outside San Francisco).
Tax is on owner of record as of 1 January and usually due in August, so if you got your AW certificate last November you now owe.
Keep in mind if you ever sell the plane in the months January - August, if you still owned the plane on 1 January you will still owe the property tax come August.
Every year, at least here in Alameda County, I get a form from the tax assessor asking about condition, avionics, etc. They also ask for the amount of hull insurance I carry.
They scan the FAA database, which is how they find you. Last year I got a letter from them, after I applied for my registration; I replied that as I did not yet have an airworthiness certificate I did not own an airplane, but rather a bunch of airplane parts. That satisfied them. However, this year, (any day now in fact) I expect to get a property tax bill, just like you.
You are free to dispute the value they placed on your aircraft; if you carry less than $115,000 in hull insurance you can probably make your case.
To add insult to injury, I lease a hangar from the city of Livermore at KLVK. State law exempts cities from paying property tax. However, the law apparently allows them to send the bill directly to the lessees (me), so I get to pay the annual property tax on the hangar, too. Fortunately it is less than $200.
CA prop 13 does not apply to airplanes, so if the market value goes up so will your tax. However, if the value goes down then make sure you get it re-assessed. I previously owned a C182 and the tax assessor actually did a pretty good job of following the market, both up and down, pretty much following the value of our hull insurance.
