JaredPar is right in that you can't know if the process is running. You can only know if the process was running at the moment you checked. It might have died in the mean time.
You also have to be aware the PIDs can be recycled pretty quickly. So just because there's a process out there with your PID, it doesn't mean that it's your process.
Have the processes share a GUID. (Process 1 could generate the GUID and pass it to Process 2 on the command line.) Process 2 should create a named mutex with that GUID. When Process 1 wants to check, it can do a WaitForSingleObject
on the mutex with a 0 timeout. If Process 2 is gone, the return code will tell you that the mutex was abandoned, otherwise you'll get a timeout.