If your process makes a system call, then while the system call code is being run in the kernel, is your process READY, RUNNING or BLOCKED?

Think of scheduling like this:

There is one copy of the kernel. When a process is the current one, the kernel "attaches" itself (called a context switch) to the process memory. So when the kernel runs a system call on behalf of the process, it is "attached", and runs in the context of the process. It's not two separate entities running.

Process states (in UNIX) are:

R - runnable which means the process has done a context switch and has the kernel.
S - sleeping which means the process is waiting on I/O completion (blocked), a pipe, memory, etc.
T - process has been stopped - sent a SIGSTOP usually with ctrl/z
Z - zombie - a process that has a process image in memory but no context, ie., not swappable.

You can see this in the ps output. If you are not on Linux an have SVR4 flavor of ps,
then you will see another "state"
O - means the process is the one that currenlty has the cpu.

What you ask has to do with system calls like read which block. I don't know what you meant by process state, since I/O blocked=one of the sleep categories