I have searched it with variations on "metal" and "detector" and "detecting", and find no prohibition. Ie.: silent on the subject. Hence not prohibited. Naturally this does not mean anyone can gripe, at any time. I mean, a man with a detector has "connotations" afterall (that you might be about to leave a mess, etc...). Thus like any park or such, you don't stick out like a sore thumb begging for attention from busy-bodies.
Also check in at the Kinzli forum. There's several So. CA folks who chime in and post there. Including a few from just that area.
Many say, by calling you've made yur first mistake? Depends on location...
Glad you received a "yes" over the phone ��, but that doesn't mean squat to groundskeepers.
Written permission and/or permits should be available upon request.
Also, please identify state in question next time.
GL
Peace ✌