If you want more details, I can scrounge. Thank you, that's generous of you. Only at your leisure, if it's not too much trouble. I've heard different information as well.
This page on the Cal. Sec. State's site is as good a starting point as any. Bottom line: voters who are registered as "decline to state" may vote in a party's primary (and presumably in only ONE party's primary per election!) IF AND ONLY IF that party has passed an internal rule permitting this. Thus far, only the AIP has done so.
No way will the two major parties allow this; they were the principal forces that sought to overturn the 1996 "open primary" amendment in the first place.