how does fork() copy threads of a process in multi-processor (SMP)

I've a general question:  In Multiprocessor (Multi-Core) (SMP) environment how does  fork system call  (do_fork() related code) maintain the synchronization in case the threads of a process are running on different processors?  E.g. it can happen that the fork() is called by cpu-0 thread and other thread of same process is executing on cpu-1. I can see that copy of the process is made by do_fork() code in fork.c.  Can anyone give more details how the concurrency issue gets handled e.g. how  PC and Regs are of cpu-1 thread get copied without any race condition in SMP / multiprocessor system? Thanks in advance