You need to read the regulations cover to cover, it is all there. It says under air rifles section (f) that rifles and pistols can be used for rabbits and squirrels. The fuzzy part is in regards to LA county but your in the Bay area so no need to worry about that unless you decide to hunt in Los Angeles County. §311. Methods Authorized for Taking Resident Small Game.Only the following may be used to take resident small game:(a) Shotguns 10 gauge or smaller using shot shells only and incapable of holding more than three shells in the magazine and chamber combined. If a plug is used to reduce the capacity of a magazine to fulfill the requirements of this section, the plug must be of one piece construction incapable of removal without disassembling the gun;(
Shotgun shells may not be used or possessed that contain shot size larger than No. BB, except that shot size larger than No. 2 may not be used or possessed when taking wild turkey. All shot shall be loose in the shell.© Muzzle-loading shotguns;(d) Falconry;(e) Bow and arrow (see Section 354 for archery equipment regulations);(f) Air rifles firing pellets and powered by compressed air or gas (0.20 caliber minimum for taking wild turkey); and firearm rifles and pistols for taking rabbits and squirrels
, except in Los Angeles County, in addition to the methods listed in (a), (
, ©, (d) and (e) above;(g) In San Diego and Orange counties only, rabbits may be taken at any time during the open season by means of box traps. Such traps shall not exceed 24 inches in any dimension, shall be tended at least once every 24 hours, and shall show the name and address of the trap owner. All rabbits taken under this section shall be immediately killed and become a part of the daily bag limit;(h) Electronic or mechanically-operated calling or sound-reproducing devices are prohibited when attempting to take resident game birds;(i) Coursing dogs may be used to take rabbits;(j) Archers hunting during any archery season may not possess a firearm while in the field engaged in archery hunting during an archery season;(k) The use of live decoys is prohibited when attempting to take resident game birds;(l) Pistols and revolvers may be used to take sooty and ruffed grouse in those counties only and for the season described in Section 300(a)(1)(E).(m) Crossbows, except for provisions of Section 354(d) and (g).(n) Dogs may be used to take and retrieve resident small game.Amended 2009.§311.6. Prohibition of Rifles and Pistols in Picacho and Providence Mountains State Recreation Areas.The use of rifles and pistols to take any bird or mammal is prohibited in Picacho and Providence Mountains State Recreation Areas.