Must I withhold taxes from payments made to independent contractors?

Yes, a California business must withhold 7% of payments made to "non-resident" independent contractors for services performed "in California". This withholding requirement does not apply to employees, or to those whom you have paid less than $1,500 in any calendar year, or for services performed out of state.

If your business fails to properly withhold the 7%, it becomes liable for that tax. See FTB publication 1023 for more info.