This is a good data sheet for this. It currently has Seattle assessed at 9.04 per 1000.00$.
I hope this helps!
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Straight property tax is $11.15 per $1000 of ASSESSED value (as James noted, this is different and usually a lower amount then appraised value). However, there can be local assessments added to this rate, which accounts for the 1.1%-1.3% range to which Rachel referred in her posting below.
.... one thing to note...i based this on actual sales data (market values) ..not assessed values. Assessed values have traditionally always been lower than market value...though counties are working to correct that. For instance, Snohomish county has gone to an annual assessment and their assessed values now are much closer ...if not really close to being market value. Anyhow, this should give you a good idea.
Check the web reference link. At the bottom of the page has a link to the tax rates in king county.