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Use the map link at the top of the page, and go from there. State maps showing rates by county are available.
Here...go to post #23 on this thread, and click on the URL he posted. The page will be non-responsive (we all know that now). In the upper right corner of the page is the BLS search box. Type in “labor participation rate” (without the quotes). This will produce a BLS search result page.
Click on the first one listed (it features the URL I gave you in my response).
Voila! There is the desired page!
But, boy - they're really making us work for it, aren't they?
CA....