Do you mean Independent, as in the American Independent Party (a CA party affiliated with the Constitution Party or seomthing), or decline-to-state, which is no party? "Independent" on the voter registration form means the AIP.
If you are Independent, then that is your party and you cannot vote in the GOP primaries. If you are decline-to-state, you can request the partisan ballot of any party that is willing to accept your vote. In March 2002, the Republicans, Democrats, and two minor parties allowed CA's no-party voters to vote the ballots of those parties. Decline-to-state voters don't get to vote for the central committee members.
The national GOP might have different views on the modified open primary for choosing the party's Presidential candidate.