Do I need to store the cord blood in the country where I plan to use it?

No.  First, you must store blood in a lab that is permitted by the regulations of the country where you will give birth.  Second, you should store cord blood in a lab that can receive and process the collection within 48 hours of birth.  After cord blood is collected at birth, the stem cells start to die while the blood is waiting to be processed and frozen.  The quicker it gets to the lab the better.  By comparison, if you ever need the cord blood for therapy, it will be shipped in a vessel that keeps it frozen.  When cord blood is released for therapy can travel to the other side of the world with no loss of viability, because it travels frozen.  It is only thawed at the clinic where it will be used.