Lee
*****
A very few. Several fistfights and a few guerilla actions (stagecoach robberies, etc), but California remained mostly pro-Union. Sufficiently so that their gold went to Washington DC rather than Richmond VA throughout the war. One resource notes that "Eighty-eight violent incidents of various sizes were fought in California, many of them against outlaws trying to capture gold for their own benefit. (No captured gold was sent to the Confederacy" but does not enumerate the "eighty-eight incidents". For the most part, California remained officially Union although a small contingent advocated secession and creation of a "Pacific Republic" in conjunction with Oregon.
Compare 88 total incidents in California to approx 750 in Arkansas ...
Exactly one (1) Confederate flag was captured in California during the Civil War (4 July 1861 - Sacramento, California) -- and the fellow who flew it (Major J. P. Gillis) was pretty poorly received by his neighbors.
See California State Military Department; The California Military Museum
http://www.militarymuseum.org/BidermanFlag.html
-kirby-