You do not need to have any DMV paperwork with you to get a smog check. The smog technician can simply enter the required information, your vehicle's vehicle identification number (VIN) and license plate number, right into the smog machine. Having the DMV renewal notice simplifies the process for the smog technician as he or she would be able to scan the bar code on the DMV document which would automatically enter the required information into the smog machine. A very few smog stations have been known to charge extra for their time to enter the vehicle information manually, however this is vary rare. I personnel would avoid a smog test center which charges extra for this process. But to answer your question; no paperwork is required to get a smog inspection in California as of this time.
In case you need to renew your vehicle's registration in California and the DMV is asking that you obtain a smog check but your vehicle is temporarily located out of state, contact NeedTags.com to complete your vehicle's registration renewal online and without a smog inspection. You will need to email them a copy of the REG 5103 (Out of State Smog Check Exemption) instead of mailing the form to the DMV, and they will be able to ship your new registration card and sticker to your out of state address instead of your California address (address on DMV records).
You may also complete the renewal process without a smog check through the DMV via mail, though the process takes approximately 30 days and your new registration card and sticker will be mailed to the address on file with the DMV. Contact NeedTags before your submit your renewal with them online, as you'll need to email them the REG 5103 prior to making your renewal payment.