You may or may not need a smog check for this title transfer. We'd recommend calling the DMV at (800) 777-0133. Vehicles which are 4 years or newer do not need a smog inspection during a title transfer. Since your Ford Mustang is a 2012 model, and if its emissions/manufacture date is 2011, you might need to have a smog inspection before they will transfer title. Check with the DMV to get accurate information pertaining to this vehicle.
We should also mention, Section 24007 (b)(2) of the Vehicle Code states it is the responsibility of the seller to provide a valid smog certificate at the time of delivery of the vehicle. You may want to advise the seller of this requirement if in fact a smog check is required.