It will depend on how you word the sentence as to which word you use.
You can say things like:
"The country whose leader is well liked by the people." "The family whose dog ran away." "The company whose CEO stole money from the clients." "The nation whose economy is in trouble."
Normally we use "that" or "which" for things. The company that I work for has international offices. The school, which is located on White Street, was given an award for excellence. The new nation in Southern Sudan, which was established after years of civil war, will be recognized by the United Nations later this year.