Dual citizenship or Permanent Residency

My mother was a Chinese citizen and Permanent Resident of the U.S. at the time of my birth. My father was born in the U.S., but returned to China in 1928 with my grandparents. My father returned to the U.S. in 1947 and my mother joined him and became a Permanent Resident of the U.S. May I apply for Dual Citizenship or Permanent Residence in China?